Question

If a – b, a and a + b are zeros of the polynomial f (x) = 2x³ – 6x² + 5x – 7, write the value of a.

Answer 1

Answer:

a=1

Step-by-step explanation:

Refer to the attachment below:

Answer 2

Answer:

a = 1

Step-by-step explanation:

Given----> ( a - b ) , a and ( a + b ) are zeroes of

f ( x ) = 2x³ - 6x² + 5x - 7

To find ----> Value of a

Solution-----> We know that ,

If a cubic polynomial

p ( x ) = ax³ + bx² + cx + d , and its zeroes are α , β , γ , then ,

α + β + γ = - Coefficient of x² / Coefficient of x³

Now , ATQ,

( a - b ) , a , ( a + b ) are zeroes of

f ( x ) = 2x³ - 6x² + 5x - 7

Now , we know that ,

Sum of zeroes = -Coefficient of x²/Coefficient ofx³

( a - b ) + a + ( a + b ) = - ( -6 ) / 2

=> 3a = 3

=> a = 3 / 3

=> a = 1

Additional information------>

1) If , p ( x ) = ax³ + bx² + cx + d , and its zeroes are α , β and γ .

α + β + γ = - Coefficient of x² / Coefficient of x³

αβ + βγ + yα = Coefficient of x / Coeficient of x³

α β γ = - Constat term / Coefficient of x³