Question 2

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

Answer

(i) Let α, β are the zeroes of the polynomial ax^{2}+ bx +c, therefore

Sum of zeroes (α + β) = 1/4 = -b/a

Product of zeroes (αβ) = -1 = c/a

On comparing,

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

Hence, the required polynomial is 4x^{2} –x – 4

(ii)

(iii)

Let α, β are the zeroes of the polynomial ax^{2}+ bx +c, therefore

Sum of zeroes (α + β) = 0 = -b/a

Product of zeroes (αβ) = √5 = √5/1 = c/a

On comparing,

a = 1, b = 0 and c = √5

Hence, the required polynomial is x^{2} + √5

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- Q:-
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- NCERT Chapter