Question

If a-b,a and b are zeros of the polynomial $f(x)=2x^{3}-6x^{2}+5x-7$,write the value of a.

Answer 1

SOLUTION :  

Let α,β,γ are the three Zeroes of the  polynomial.

Given : f(x) = 2x³ - 6x² + 5x -7

α = a - b , β = a , γ = b

On comparing with ax³ + bx² + cx + d ,

a = 2 , b = -6 , c = 5 , d = -7

Sum of zeroes of cubic POLYNOMIAL = −coefficient of x² / coefficient of x³

α + β + γ = −b/a

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

a + a + a = 3

3a = 3

a = 3/3  

a = 1

Hence, the value of a is 1.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

SOLUTION :  

Let α,β,γ are the three Zeroes of the  polynomial.

Given : f(x) = 2x³ - 6x² + 5x -7

α = a - b , β = a , γ = b

On comparing with ax³ + bx² + cx + d ,

a = 2 , b = -6 , c = 5 , d = -7

Sum of zeroes of cubic POLYNOMIAL = −coefficient of x² / coefficient of x³

α + β + γ = −b/a

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

a + a + a = 3

3a = 3

a = 3/3  

a = 1

Hence, the value of a is 1.

HOPE THIS ANSWER WILL HELP YOU.

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