Question

If α, β are the zeros of the polynomial p(x) = 4x² + 3x + 7, then (1/α) + (1/β) =
A. 7/3
B. -7/3
C. 3/7
D. -3/7

Answer 1

Answer:

( D ) ( - 3 / 7 )

Step-by-step explanation:

Given-----> α and β are the zeroes of the polynomial p ( x ) = 4x² + 3x + 7

To find -----> Value of ( 1/α + 1/β )

Solution------> We know that , if ,

f ( x ) = ax² + bx + c , is quadratic polynomial and α and β are its zeroes then ,

α + β = - Coefficient of x / Coefficient of x²

α β = Constant term / Coefficient of x²

Now , ATQ,

P ( x ) = 4x² + 3x + 7 and zeroes of it is α and β .

α + β = - Coefficient of x / Coefficient of x²

=> α + β = - 3 / 4

α β = Constant term / Coefficient of x²

=> αβ = 7 / 4

Now we have to find value of ,

1 / α + 1 / β = ( α + β ) / αβ

Putting α + β = - 3 / 4 and αβ = 7 / 4 , we get,

1 / α + 1 / β = ( -3/4 ) / ( 7/4 )

=> 1/α + 1/β = - 3/7

So ( D ) is correct answer