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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  α,β \alpha, \beta are the zeros of the polynomial  x2px+36 x^2 - px + 36 and  α2+β2=9 \alpha^2 + \beta^2 = 9 , then  p= p = Select an answer

A  ±6
B  ±3
C  ±8
D  ±9

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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.

This problem has been solved

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