Question

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

Answer 1

Answer:

15/4

Step-by-step explanation:

α+β= -(-1/1)=1

αβ= -4/1= -4

1/α+1/β-αβ= α+β/αβ- αβ= 1/(-4) +4 = -15/-4 = 15/4 ans

Answer 2

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…

 

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