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

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.