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If the zeroes of the polynomial p(x) = x² − kx + 36 are positive and in the ratio 1:4, what is the value of k?

Answer and explanation

Correct answer: 15

Let the zeroes be t and 4t. Their product is 36, so 4t² = 36. Since both zeroes are positive, t = 3, giving zeroes 3 and 12. Their sum is 15; for x² − kx + 36, the sum of the zeroes is k. Therefore, k = 15.

Related tags

PolynomialsZeroes And CoefficientsRatio Of ZeroesPolynomials In One VariableMathematicsClass 10 Mcq

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