Question

If a and B are zeroes and the quadratic
polynomial f(x) = x2 - X - 4, then the value
of a÷ß +1÷b is
-15
(a)15÷4
(b)-15÷4
(d) 15
(c) 4​

Answer 1

Correct question:-

If a and are the zeros of the quadratic polynomial f(x) = x² − x − 4, find the value of 1/α +1/β-αβ .

Given:-

p(X) = x²-x-4

Solution:-

α+β = $\sf\dfrac{-b}{a}$ = 1

αβ = $\sf\dfrac{c}{a}$ = -4

$\sf\dfrac{1}{α}$ + $\sf\dfrac{1}{β}$ - αβ

$\sf\dfrac{α+β}{αβ}$ - αβ

$\sf\dfrac{1}{-4}$ - (-4 )

$\sf\dfrac{-1+16}{4}$

$\sf\dfrac{15}{4}$