If α, β are the zeros of the polynomial x2 − px + 36 and α2 + β2 = 9 , then p = Select an answerA ±6 B ±3 C ±8 D ±9
Question
If are the zeros of the polynomial and , then Select an answer
A ±6
B ±3
C ±8
D ±9
Solution
Given that α and β are the zeros of the polynomial x² - px + 36, we know from Vieta's formulas that:
- α + β = p (the sum of the roots is equal to the negation of the coefficient of x, which is -p)
- αβ = 36 (the product of the roots is equal to the constant term, which is 36)
We are also given that α² + β² = 9. We can express α² + β² in terms of α + β and αβ using the identity α² + β² = (α + β)² - 2αβ. Substituting the values we have:
9 = p² - 2*36 9 = p² - 72 p² = 9 + 72 p² = 81
Taking the square root of both sides, we get p = ±9.
So, the answer is D ±9.
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