Question

find a quadratic polynomial each with the given numbers as sum and product of its zeros respectively
$\sqrt{2} \\ - \frac{3}{2}$
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Answer 1

Solution :-

Let α, β be the zeroes of the polynomial

Given :-

• Sum of zeroes = α + β = √2
• Product of zeroes = αβ = - 3/2

We know that

Quadratic polynomial = k{ x² - x(α + β) + αβ }

[ Where k ≠ 0 and α,β are the zeroes of the polynomial ]

= k{ x² - x(√2) + (-3/2) }

= k(x² - √2 x - 3/2)

= k{ (2x² - 2√2 x - 3)/2 }

When k = 2

= 2{ (2x² - 2√2 x - 3)/2 }

= 2x² - 2√2 x - 3

Therefore the polynomial is 2x² - 2√2 - 3