Question

For each of the following , find a quadratic polynomial whose sum and product respectively of the zeroes are as given . also find the zeroes of these polynomial by factorisation. -3 / 2 root 5 , -1/2

Answer 1

Given :- For each of the following , find a quadratic polynomial whose sum and product respectively of the zeroes are as given . Also find the zeroes of these polynomial by factorisation.

• -3 / 2√5 , -1/2

Answer :-

we know that, a quadratic equation with sum and product of zeros can be written as ,

• x² - (sum of zeros) * x + product of zeros = 0 .

given that,

• sum of zeros = (-3/2√5)
• Product of zeros = (-1/2) .

so,

→ Required quadratic polynomial = x² - (-3/2√5)x + (-1/2) = 0

→ x² + (3/2√5)x - (1/2) = 0

→ (2√5x² + 3x - √5) / 2√5 = 0

→ 2√5x² + 3x - √5 = 0

now, factorisation :-

→ 2√5x² + 3x - √5 = 0

→ 2√5x² + 5x - 2x - √5 = 0

→ √5x(2x + √5) - 1(2x + √5) = 0

→ (2x + √5)(√5x - 1) = 0

putting both equal to zero, we get,

→ 2x + √5 = 0

→ 2x = (-√5)

→ x = (-√5/2) (Ans.)

and,

→ √5x - 1 = 0

→ √5x = 1

→ x = (1/√5) (Ans.)

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