If (a-b) and (a+b) are the zeros of the polynomial f(x) =2x³-6x²+5x-7.find the value of a
Answers
we know that
sum of zeroes=-b/a
a-b+a+b=-(-6 )/2
2a=3
a=3/2
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