Question

find the quadratic polynomial whose sum and product of it's zeroes are ⅓,4 respectively
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Answer 1

Answer :

3x² + x + 12

Solution :

Let, the zeroes of polynomial be α, β.

Given,

sum of zeroes, α + β = 1/3

product of zeroes, αβ = 4

Quadratic polynomial,

p(x) = x² + (α + β)x + αβ

→ x² + 1/3x + 4

→ 3x² + x + 12

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Answer 2

AnswEr :-

• The quadratic polynomial is 3x² - x + 12.

Given :-

• Sum of the zeroes of a quadratic polynomial is 1/3.

• Product of the zeroes of the quadratic polynomial is 4.

To Find :-

• The quadratic polynomial.

Solution :-

• α + β = 1/3

• α × β = 4

Formula of the quadratic polynomial is :-

p(x) = x² - (sum of zeroes)x + product of zeroes

→ x² - (α + β)x + (α × β)

→ x² - (1/3)x + (4)

→ x² - 1/3x + 4

→ 3x² - x + 12 [ multiply whole equation by 3 ]

Hence, the quadratic equation is 3x² - x + 12.

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