Question

the roots of equation x2 + px + q =0 are equal if​

Answer 1

Answer:

p^2=4q

Step-by-step explanation:

for roots to be equal we have to equate the discriminant to 0

p^2-4q=0

p^2=4q

Answer 2

Answer:

The roots of x² + px + q = 0 are equal if discriminant (D) is p² - 4q.

Step-by-step explanation:

In order to have equal roots the discriminant (D) of a quadratic equation should be zero.

For a quadratic equation $ax^2 + bx + c = 0$

$D = \sqrt{b^2 - 4ac}$

We have to find the discriminant (D) is x² + px + q = 0

On comparing ax² + bx + c = 0 to x² + px + q = 0 we get,

a = 1

b = p

c = q

$D = \sqrt{b^2 - 4ac}$

$\implies D = \sqrt{p^2 - (4*1*q)}$

$\implies D = \sqrt{p^2 - 4q}$

∴ The roots of x² + px + q = 0 are equal if discriminant (D) is p² - 4q.

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