Question

If -1 and 3 are the roots of ×square+p×+q=0, find the values of p and q.

Answer 1

Answer :

p = -2

q = -3

Given :

◘ Quadratic equation, x² + px + q = 0

◘ -1 and 3 are zeroes of the polynomial.

To find :

◘ Values of p and q

Solution :

• -1 is zero of the polynomial,

Put x = -1,

⇒ x² + px + q = 0

⇒ (-1)² + p(-1) + q = 0

⇒ 1 - p + q = 0

⇒ p - q = 1

$\boxed{So,p-q=1}$             ----> equation (1)

• 3 is zero of the polynomial,

Put x = 3,

⇒ x² + px + q = 0

⇒ 3² + p(3) + q = 0

⇒ 9 + 3p + q = 0

⇒ 3p + q = -9

$\boxed{So,3p+q=-9}$          ----> equation (2)

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From equations (1) and (2),

 p - q = 1

3p + q = -9

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4p = -8

 p = -8/4

 p = -2

Substitute value of p in any equation,

I am substituting in equation (1)

p - q = 1

-2 - q = 1

-q = 1 + 2

-q = 3

 q = -3

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HOPE IT HELPS..!