If α and β, α > β, are the zeroes of the polynomial p (x) = 2x² - 5x + k such that \(\rm \alpha-\beta=-\frac{7}{2}\)then k is a zero of which of the following polynomials?

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AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)

Answer 1

Given:

Polynomial: p(x) = 2x² - 5x + k

Zeroes: α and β, α > β

α - β = -7/2

Formula used:

Sum of zeroes: α + β = -b/a

Product of zeroes: αβ = c/a

Calculation:

Sum of zeroes: α + β = 5/2

Given that, α - β = -7/2

⇒ (α + β) + (α - β) = 5/2 - 7/2

⇒ 2α = -1 ⇒ α = -1/2

⇒ β = 5/2 - (-1/2) ⇒ β = 3

Product of zeroes: αβ = -1/2 × 3

⇒ -3/2 = k/2

⇒ k = -3

k is a zero of the polynomial x² + 2x - 3

∴ The correct answer is option (3).

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