Question

Answer:- Given:- α , β are the roots of p(y) = y² - 8y + a. On comparing the given polynomial with the standard form of a quadratic equation i.e., ax² + bx + c = 0 ; Let, a = 1 b = - 8 c = a. We know that, Sum of the roots = - b/a ⟹ α + β = - ( - 8)/1 ⟹ α + β = 8 -- equation (1). Product of the roots = c/a ⟹ αβ = a/1 ⟹ αβ = a -- equation (2) It is also given that, ⟹ α² + β² = 40 using a² + b² = (a + b)² - 2ab in LHS we get, ⟹ (α + β)² - 2αβ = 40 Substituting the respective values from equations (1) & (2) we get, ⟹ 8² - 2a = 40 ⟹ 64 - 40 = 2a ⟹ 24/2 = a ⟹ a = 12 ∴ The value of a is 12.​

Answer 1

Answer:

ur answer is 12

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