Question

If -1 and 3 are the roots of x²+px+q=0
then find the values of p and q

Answer 1

Since -1 is a root of x2 + px + q = 0, we have

(-1)² + p(-1) + q = 0

⇒ 1 - p + q = 0

⇒ -p + q = -1.......(i)

Also, 3 is a root of x² + px + q = 0

⇒ (3)² + p(3) + q = 0

⇒ 9 + 3p + q = 0

⇒ 3p + q = -9.......(ii)

Subtracting equation (ii) from (i), we get

-4p = 8

⇒ p = -2

⇒ -(-2) + q = -1     ...........[From (i)]

⇒ 2 + q = -1

⇒ q = -3

Hence, p = -2 and q = -3