Question

If α and β are the zeroes of a quadratic polynomial such that α + β = 24 and

α – β = 8 , find quadratic polynomial having α and β as its zeroes. Verify the

relationship between the zeroes and the coefficient of the polynomial.​

Answer 1

α and β are the zeroes of a quadratic polynomial.

α + β = 24 ………..> (1)

α – β = 8 …………..> (2)

Adding (1) + (2) we get 2α =32 ⇒ α = 16

Subtraction (1) & (2) we get 2β =16 ⇒ β = 8

The quadratic polynomial having α and β as its zeroes is

k{x2-(α+β)x+αβ}, where k is real.

⇒ K{ x2–(16+8)x + (16)(8)} , k is a real

⇒ K{x2-24x+128) , k is a real

⇒ K x2-24kx+128k, k is real

Comparing with ax2

+bx+c , we get a = k ,b = -24k, c = 128k

Answer 2

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Upper answer is right ...no need more explanation✌️ ❤️

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