Question

if alpha and beta are the zeros of polynomial X square + 7 x + 12 then find the value of alpha + beta + 2 alpha beta​

Answer 1

Given :-

${x^2+7x+12=0}$

From this equation, we get

a = 1; b = 7; c = 12

To find:-

Let alpha be 'a' and beta be 'b'

(a + b) + 2(ab)

Proof :-

Now, Sum of roots (a+b) = ${\dfrac{-b}{a}}$

Therefore, a + b = -7......(1)

Product of roots(ab) =${\dfrac{c}{a}}$

Therefore, ab = 12.....(2)

Substituting (1) & (2) in the To Prove equation, we get,

(a + b) + 2(ab)

-» (-7) + 2(12)

-» -7 + 24

-» 17

Therefore, a + b + 2ab = 17