Question

Please answer this question ​

Answer 1

Answer :-

Value of k is 12.

Step-by-step explanation :-

Given :

f(x) = x² - 8x + k

α² + β² = 40

To find :

Value of k ?

Solution :

Sum of zeroes :

α + β = -b/a

α + β = -8/a

α + β = -8 (1)

Product of zeroes :

α × β = c/a

α × β = k/1

α × β = k (2)

We know that :

(a + b)² = a² + b² + 2ab

(α + β)² = 40 + 2αβ

Using (1) and (2) :

(-8)² = 40 + 2αβ

64 = 40 + 2αβ

24 = 2k

∴ k = 12