If α and β be the zeroes of the polynomial x2 + 11x + k , where α2 + β2 = 115 , then the value of k Select an answerA1B2C3D6
Question
If α and β be the zeroes of the polynomial x² + 11x + k , where α² + β² = 115 , then the value of k
Select an answer
A. 1
B. 2
C. 3
D. 6
Solution
The zeroes of the polynomial x² + 11x + k are α and β.
According to Vieta's formulas, the sum of the zeroes (α + β) is equal to -b/a = -11/1 = -11 and the product of the zeroes (α*β) is equal to c/a = k/1 = k.
Given that α² + β² = 115, we can express this in terms of the sum and product of the zeroes as follows:
α² + β² = (α + β)² - 2αβ 115 = (-11)² - 2*k 115 = 121 - 2k 2k = 121 - 115 2k = 6 k = 6/2 k = 3
So, the value of k is 3. The correct answer is C3.
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