Question

Find a quadrtic polynomial each with the given numbers as the sum and prodct of its zeroes respectely.

(i) 1/4, -1

(ii) 1,1

(iii) 4, 1​

Answer 1

Answer:

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Answer 2

$\huge\underline\mathrm{Question}:-$

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i) 1/4, -1

(ii) 1,1

(iii) 4, 1

$\huge\underline\mathrm{Solution}:-$

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

Sum of zeroes = α + β

Sum of zeroes = α + βProduct 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.

(ii) Given,

Sum of zeroes = α + β = 1

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 – x + 1 = 0

Thus, x²– x + 1 is the quadratic polynomial.

(iii) Given,

Sum of zeroes = α + β = 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– 4x +1 = 0

Thus, x²- 4x +1 is the quadratic polynomial.