Question

If m and n are roots of the equation x${}^2$ + 3x - 14 = 0 then Find m${}^3$ + n${}^3$

• A. 99
• B. -153
• C. 153
• D. -99
• E. Cannot be determined

Answer 1

The correct option is B -153

m${}^3$ + n${}^3$ = (m + n)${}^3$ - 3nm${}^2$ - 3mn${}^2$ = (m+n)${}^3$ - 3mn (m + n)

Sum of roots, m+n = $-\frac{b}{a}$ = -3

Product of roots, mn = $\frac{c}{a}$ = -14

So, m${}^3$ + n${}^3$ = (-3)${}^3$ - (3$\times$ -14$\times$ -3) = -27 - 126 = -153