Question

find the quadratic polynomian if the sum and product of its zeroes are respectively -1/4,1/4

Answer 1

Let the zeroes be A and B

Given , A+B=-1/4 and AB=1/4

So the polynomial will be

p (x)=x^2-(A+B) x+(AB)

=x^2+1/4x+1/4

reqUired eq. Is 4x^2+x+1

Answer 2

Solution :

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Quadratic polynomial whose zeroes

are m , n is

k[ x² - ( m + n )x + mn ]

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Here ,

m + n = -1/4 ,

mn = 1/4

Now ,

Required Quadratic polynomial is

k [ x² - (-1/4)x + 1/4 ]

= k[ x² + x/4 + 1/4 ]

For all values of k it is true ,

if we take k = 4 , then

= 4x² + x + 1

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