If  α, β  are zeroes of  x2 − 6x + k , what is the value of  k  if  4α + 5β  =  32  ?Select an answerA–16B8C2D–8

To solve this problem, we need to use the relationship between the roots and the coefficients of a quadratic equation.

The sum of the roots (α + β) is equal to -b/a, and the product of the roots (α*β) is equal to c/a, where a, b, and c are the coefficients of the quadratic equation.

In this case, the quadratic equation is x² - 6x + k. So, a = 1, b = -6, and c = k.

From the equation 4α + 5β = 32, we can express α in terms of β: α = (32 - 5β)/4.

Since α + β = -b/a = 6, we can substitute α in this equation: (32 - 5β)/4 + β = 6. Solving this equation for β, we get β = 2.

Substituting β = 2 into the equation α = (32 - 5β)/4, we get α = 4.

Finally, since αβ = c/a = k, we get k = 42 = 8.

So, the correct answer is B. 8.