Name: Standard Form of a Quadratic Equation
Uploaded: 2019-07-19
Duration: 9 min 11 s
Description: This video teaches you about the standard form of a quadratic equation. This represents a parabola in coordinate geometry. Start learning the concept.

Question

Write three quadratic equations one having two distinct real solutions, one having no real solution and one having exactly one real solution.

Accepted Answer

Here, we need to write three quadratic equations one having two distinct real solutions, one having no real solution and one having exactly one real solution.

For a quadratic equation $a x^{2} + b x + c = 0$ where, $a \neq 0$ , $b^{2} - 4 a c$ is known as discriminant.

If $b^{2} - 4 a c = 0$ , then equation has two distinct real roots.

If $b^{2} - 4 a c > 0$ , then equation has two equal roots.

If $b^{2} - 4 a c < 0$ , then equation has no real roots.

For $2 x^{2} - 3 x + 2 = 0$ ,

$b^{2} - 4 a c = {(- 3)}^{2} - 4 (2) (2) = 9 - 16 = - 7 < 0$

For $x^{2} - 5 x + 6 = 0$ ,

$b^{2} - 4 a c = {(- 5)}^{2} - 4 (1) (6) = 25 - 24 = 1 > 0$

For $z^{2} - 8 z + 16 = 0$

$b^{2} - 4 a c = {(- 8)}^{2} - 4 (1) (16) = 64 - 64 = 0$

Hence, quadratic equation having two distinct real solutions, no real solution and exactly one real solution are $x^{2} - 5 x + 6 = 0, 2 x^{2} - 3 x + 2 = 0$ and $z^{2} - 8 z + 16 = 0$ respectively.

Write three quadratic equations one having two distinct real solutions, one having no real solution and one having exactly one real solution.

Important Questions on Quadratic Equations

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