Question

Frame the quadratic polynomial whose zeroes are 1/4 and -1

Answer 1

Step-by-step explanation:

Given:-

Zeroes are 1/4 and -1

To find:-

Frame the quadratic polynomial whose zeroes are 1/4 and -1 ?

Solution:-

Given that

Zeroes are 1/4 and -1

Let they be

α = 1/4

β = -1

We know that

The quadratic polynomial whose zeroes α and β is K[x^2- (α+ β)x +α β]

On Substituting these values in the above formula

=>K[x^2-(1/4 +(-1))x +(1/4)(-1)]

=>K[x^2-(1/4-1)x-(1/4)(1)]

=>K[x^2-{(1-4)/4}x -(1/4)]

=>K[x^2-(-3/4)x-(1/4)]

=>K[(4x^2-3x-1)/4]

=>(K/4)[4x^2-3x-1]

If K = 4 then the required Polynomial is

4x^2-3x-1

Answer:-

The required quadratic polynomial for the given problem is 4x^2-3x-1

Used formulae:-

• The quadratic polynomial whose zeroes α and β is K[x^2- (α+ β)x +α β]