Question

(x-a) (x-b) = x^2+x+4 then 1/a^2 +1/b^2​

Answer 1

Answer:

(x−a)(x−b)−1=0

⇒x

2

−(a+b)x−ab−1=0

then discriminant is (a+b)

2

−4(ab−1)=(a−b)

2

+4>0,

it has two real roots further f(a)=−1 and f(b)=−1 but b>a i.e a and b are distinct as coefficient of x

2

is position (it is 1), minima of f(x) is between a and b

Hence, one root will be in the interval (−α,a) and the other root will be in the interval (b,α).