Question

If $\alpha and \beta$ are the zeros of the quadratic polynomial $f(y)= x^{2}-x-4$,find the value of $\frac{1}{\alpha} +\frac{1}{\beta} -\alpha \beta$

Answer 1

SOLUTION :

Given : α and β are the zeroes of the quadratic polynomial f(x)= x² - x - 4

On comparing with ax² + bx + c,

a = 1 , b= -1 , c= -4

Sum of the zeroes = −coefficient of x / coefficient of x²

α + β  = -b/a = -(-1)/1 = 1  

α+β = 1……………………..(1)

Product of the zeroes = constant term/ Coefficient of x²

αβ = c/a = -4/1 = - 4

αβ = - 4 ……………………(2)

1/α + 1/β  - αβ =[( α+β) / αβ] - αβ

By Substituting the value from eq 1 & eq2 , we get  

=[ 1/−4 ]  - (- 4)

= −1/4 + 4

= (−1+16)/4 =

=  15/ 4

1/α + 1/β  - αβ  = 15/4

Hence, the value of  1/α + 1/β  - αβ  = 15/4

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

x^2 - x- 4=?

To find 1/alpha + 1/beta - alpha beta

alpha + beta = 1

alpha × beta = -4

1/alpha + 1/beta = ( beta + alpha)/ alpha beta = -1/4

So 1/alpha + 1/beta - alpha beta
= -1/4 - ( -4)

= -1/4 + 4

= 15/4