Quadratic Equation does not pass through the x-axis [closed]
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If a quadratic equation does not pass through the x-axis, what can you say about its discriminant and the solutions of the quadratic equation?
linear-algebra
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
closed as off-topic by José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy Nov 24 at 16:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
If a quadratic equation does not pass through the x-axis, what can you say about its discriminant and the solutions of the quadratic equation?
linear-algebra
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
closed as off-topic by José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy Nov 24 at 16:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
The solutions are imaginary and the discriminant is smaller than 0.
– Mohammad Zuhair Khan
Nov 24 at 7:36
Thank, I will. It is so cool.
– Ehsan Zehtabchi
Nov 24 at 8:02
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If a quadratic equation does not pass through the x-axis, what can you say about its discriminant and the solutions of the quadratic equation?
linear-algebra
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
If a quadratic equation does not pass through the x-axis, what can you say about its discriminant and the solutions of the quadratic equation?
linear-algebra
linear-algebra
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
asked Nov 24 at 7:35
Ehsan Zehtabchi
263
263
closed as off-topic by José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy Nov 24 at 16:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy Nov 24 at 16:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Batominovski, Davide Giraudo, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
The solutions are imaginary and the discriminant is smaller than 0.
– Mohammad Zuhair Khan
Nov 24 at 7:36
Thank, I will. It is so cool.
– Ehsan Zehtabchi
Nov 24 at 8:02
add a comment |
The solutions are imaginary and the discriminant is smaller than 0.
– Mohammad Zuhair Khan
Nov 24 at 7:36
Thank, I will. It is so cool.
– Ehsan Zehtabchi
Nov 24 at 8:02
The solutions are imaginary and the discriminant is smaller than 0.
– Mohammad Zuhair Khan
Nov 24 at 7:36
The solutions are imaginary and the discriminant is smaller than 0.
– Mohammad Zuhair Khan
Nov 24 at 7:36
Thank, I will. It is so cool.
– Ehsan Zehtabchi
Nov 24 at 8:02
Thank, I will. It is so cool.
– Ehsan Zehtabchi
Nov 24 at 8:02
add a comment |
2 Answers
2
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When a quadratic function never crosses the $x$-axis, then it has no real roots or solutions. Hence, the discriminant must be negative.
$$Delta = b^2-4ac$$
No real solution means
$$Delta < 0$$
which is the same as
$$b^2-4ac < 0$$
meaning the solutions are imaginary/complex.
answered Nov 24 at 7:39
KM101
3,960417
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Since we have not real solutions $Delta=b^2-4ac<0$, more in detail we have two cases
for $a>0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave up above the $x$-axis
for $a<0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave down under the $x$-axis
Refer also to the raleted
- Quadratic Equations with Complex Roots
answered Nov 24 at 7:47
gimusi
1
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
When a quadratic function never crosses the $x$-axis, then it has no real roots or solutions. Hence, the discriminant must be negative.
$$Delta = b^2-4ac$$
No real solution means
$$Delta < 0$$
which is the same as
$$b^2-4ac < 0$$
meaning the solutions are imaginary/complex.
answered Nov 24 at 7:39
KM101
3,960417
add a comment |
up vote
1
down vote
accepted
When a quadratic function never crosses the $x$-axis, then it has no real roots or solutions. Hence, the discriminant must be negative.
$$Delta = b^2-4ac$$
No real solution means
$$Delta < 0$$
which is the same as
$$b^2-4ac < 0$$
meaning the solutions are imaginary/complex.
answered Nov 24 at 7:39
KM101
3,960417
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
When a quadratic function never crosses the $x$-axis, then it has no real roots or solutions. Hence, the discriminant must be negative.
$$Delta = b^2-4ac$$
No real solution means
$$Delta < 0$$
which is the same as
$$b^2-4ac < 0$$
meaning the solutions are imaginary/complex.
answered Nov 24 at 7:39
KM101
3,960417
When a quadratic function never crosses the $x$-axis, then it has no real roots or solutions. Hence, the discriminant must be negative.
$$Delta = b^2-4ac$$
No real solution means
$$Delta < 0$$
which is the same as
$$b^2-4ac < 0$$
meaning the solutions are imaginary/complex.
answered Nov 24 at 7:39
KM101
3,960417
answered Nov 24 at 7:39
KM101
3,960417
answered Nov 24 at 7:39
KM101
3,960417
answered Nov 24 at 7:39
KM101
3,960417
3,960417
add a comment |
add a comment |
up vote
0
down vote
Since we have not real solutions $Delta=b^2-4ac<0$, more in detail we have two cases
for $a>0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave up above the $x$-axis
for $a<0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave down under the $x$-axis
Refer also to the raleted
- Quadratic Equations with Complex Roots
answered Nov 24 at 7:47
gimusi
1
add a comment |
up vote
0
down vote
Since we have not real solutions $Delta=b^2-4ac<0$, more in detail we have two cases
for $a>0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave up above the $x$-axis
for $a<0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave down under the $x$-axis
Refer also to the raleted
- Quadratic Equations with Complex Roots
answered Nov 24 at 7:47
gimusi
1
add a comment |
up vote
0
down vote
up vote
0
down vote
Since we have not real solutions $Delta=b^2-4ac<0$, more in detail we have two cases
for $a>0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave up above the $x$-axis
for $a<0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave down under the $x$-axis
Refer also to the raleted
- Quadratic Equations with Complex Roots
answered Nov 24 at 7:47
gimusi
1
Since we have not real solutions $Delta=b^2-4ac<0$, more in detail we have two cases
for $a>0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave up above the $x$-axis
for $a<0$ and $b^2-4ac<0$ the equation $y=ax^2+bx+c$ represent a parabola concave down under the $x$-axis
Refer also to the raleted
- Quadratic Equations with Complex Roots
answered Nov 24 at 7:47
gimusi
1
answered Nov 24 at 7:47
gimusi
1
answered Nov 24 at 7:47
gimusi
1
answered Nov 24 at 7:47
gimusi
1
1
add a comment |
add a comment |
The solutions are imaginary and the discriminant is smaller than 0.
– Mohammad Zuhair Khan
Nov 24 at 7:36
Thank, I will. It is so cool.
– Ehsan Zehtabchi
Nov 24 at 8:02