Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 1/4, -1​

Answer 1

Step-by-step explanation:

sum of zeroes = -b / a

1/4 = - b / a. equation_____ 1

product of zeroes = c / a

-1 = c /a. equation _______ 2

For making quadratic equation we have to multiply equation 2nd by 4 -

-1 /1 × 4/4 = - 4/4

now we have --

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

so quadratic equation is ----

4x ^ 2 -1x- 4 OR

four x square minus one x minus 4.

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Answer 2

Answer:

From the formulas of sum and product of zeroes, we know,

Sum of zeroes = α+β

Product of zeroes = α β

Sum of zeroes = α+β = 1/4

Product of zeroes = α β = -1

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-

x²–(α+β)x +αβ = 0

x²–(1/4)x +(-1) = 0

4x²–x-4 = 0

Thus,4x²–x–4 is the quadratic polynomial.

Step-by-step explanation:

Hope this helps you ✌️