Question

if alpha and beta are the zeros of the polynomial p x = x square - px + 36 and Alpha square + beta square = 9 then the value of P is:

a) 6 b) 3 c) 8 d) 9

Answer 1

EXPLANATION.

α and β are the zeroes of the polynomial.

⇒ p(x) = x² - px + 36.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = -b/a.

⇒ α + β = -(-p/1).

⇒ α + β = p.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = 36.

To find : Value of p.

⇒ α² + β² = 9.

⇒ (α + β)² - 2αβ = 9.

Put the values in the expression, we get.

⇒ (p)² - 2(36) = 9.

⇒ p² - 72 = 9.

⇒ p² = 9 + 72.

⇒ p² = 81.

⇒ p = ±√81.

⇒ p = 9.

Value of p = 9.

Option [D] is correct answer.

                                                                                                                 

MORE INFORMATION.

D = discriminant Or b² - 4ac.

(1) If D < 0.

One roots : α + iβ.

Other roots : α - iβ.

(2) If D > 0.

One roots : α + √β.

Other roots : α - √β.