Question

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

Answer 1

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1) 1/4 , -1

Given

Alpha + beta =1/4

Alpha ×beta =1

x^2 -(aplha +beta)x + aplha×beta

Putting constant term as K

K(x^2 -(aplha +beta)x + aplha×beta)

Now putting the values

K( x^2-1/4x + (-1)=0

So we get ,

K ( x^2-1/4x -1)=0

Or

By dividing 4 we get

K (4x^2-x-4)=0

Answer 2

Answer:

$\huge\bf\underline{\underline{Answer}}$

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 = $\frac{1}{4}$

• 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 –($\frac{1}{4}$ )x +(-1) = 0

➡ 4x² –x-4 = 0

Thus,4x² –x–4 = 0 is the quadratic polynomial.