Question

If the roots of the equation x^2+px+7=0 are donated by alpha and beta ,and a^2+b^2=22,find the possible value of p.

Answer 1

Answer:

Given polynomial => x² + px + 7 = 0

let , a = 1 ; b = p ; c = 7

a² + b² = 22

We know that,

Sum of the roots (a + b) = - b/a

a + b = - p/1 = - p

Product of the roots (ab) = c/a

ab = 7/1 = 7.

We know that,

a² + b² = (a + b)² - 2ab. [ a² + b² + 2ab - 2ab]

=> 22 = (- p)² - 2(7)

22 = p² - 14

p² = 22 + 14

p² = 36

p = √36

p = ± 6

Hence, the value of "p" is ± 6.