Question

find the quadratic polynomial each with the given numbers as the sum and product of its zeros respectively 1/4,-1​

Answer 1

Solution :-

Given :

Sum of zeros = α + β = 1/4

product of zeros = αβ = - 1

Formula to form quadratic polynomial :

x² - (Sum of zeros)x + product of zeros

= x² - 1/4x - 1

Hence,

Quadratic polynomial = f(x) = x² - 1/4x - 1

Answer 2

Questions—

Find the quadratic polynomial each with the given numbers as the sum and product of its zeros respectively 1/4,-1.

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4x² - x - 4

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Given—

Sum of roots(α + β) = 1/4

Product of roots(αβ) = - 1

To find —

The Quadratic polynomial

Solution—

Let the polynomial be ax²+bx+c____(1)

We know

α + β= -b/a

αβ = c/a

Comparing with given

-b/a = 1/4

c/a = - 1

Therefore, a= 4, b =1, c = - 4

Hence by putting in eq 1 the polynomial be

4x² - x - 4

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