Question

Find the zeros of the quadratic polynomial and verify the relationship between the zeroes and coefficient
x2-1
​

Answer 1

Answer:

2ab

Step-by-step explanation:

Let f(x)=x

2

−(2a+b)x+2ab

f(x)=x

2

−2ax−bx+2ab

=x(x−2a)−b(x−2a)

=(x−2a)(x−b)

On putting f(x)=0, we get

(x−2a)(x−b)=0

⇒x−2a=0 or x−b=0

⇒x=2a or x=b

Thus, the zeroes of the given polynomial x

2

−(2a+b)x+2ab are 2a and b

Verification :

Sum of zeroes =α+β=2a+b or

=−

Coefficient of x

2

Coefficient of x

=−

1

(−2a−b)

=2a+b

Product of zeroes =αβ=2a×b=2ab or

=

Coefficient of x

2

Constant term

=

1

2ab

=2ab

So, the relationship between the zeroes and the coefficients is verified.