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