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Answer» Given α and β are the zeroes of the polynomial x^2− 2x + kAlso given that α − β = 8 → (1)Recall that sum of roots (α + β) = −(b/a)∴ α + β = 2 → (2)Add (1) and (2), we getα − β = 8α + β = 22α = 10∴ α = 5Put α = 5 in α + β = 25+ β = 2∴ β = -3Since 5 and -3 are zeroes of the given polynomialPut x = 5 in the given polynomial to find the value of kx^2− 2x + k⇒ 5^2− 2(5) + k = 0⇒ 35− 10 + k = 0⇒ 25+ k = 0∴ k = 25 |
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