If the roots of the equation $x^2 - 10x + k - 1 = 0$ are α and β and $α^3 + β^

If the roots of the equation $x^2 - 10x + k - 1 = 0$ are α and β and $α^3 + β^3 = 70$,
then find the value of k.

A. 32

B. 30

C. 16

D. 70

E. None of the above

Answer: A. 32

Here, the roots of the equations $x^2 - 10x + k - 1 = 0$ are α and β:
Thus, α + β = ${-b}/a = (-10)/1 = 10$ and $αβ = c/a = {k - 1}/1 = k - 1$
Now $α^3 + β^3 = 70$
.`. $(α + β)^3 - 3αβ(α + β) = 70$
.`. $(10)^3 - 3(k - 1)(10) = 70$
.`. 100 - 3k + 3 = 7
.`. 100 - 4 = 3k
.`. 96 = 3k
.`. k = $96/3$
.`. k = 32

Posted in: Quadratic Equations - Algebra - Mathematics

If the roots of the equation $x^2 - 10x + k - 1 = 0$ are α and β and $α^3 + β^3 = 70$,then find the value of k.

If the roots of the equation $x^2 - 10x + k - 1 = 0$ are α and β and $α^3 + β^3 = 70$,
then find the value of k.