Question

Find the value of k such that
5/2 is a root of the quadratic equation 14x² – 27x + k=0.​

Answer 1

$14 {x}^{2} - 27x + k = 0 \\ 14 {( \frac{5}{2} )}^{2} - 27( \frac{5}{2} ) + k = 0 \\ (14 \times \frac{25}{4} ) - (27 \times \frac{5}{2} ) + k = 0 \\ \frac{175}{2} - \frac{135}{2} + k = 0 \\ \frac{175 - 135}{2} + k = 0 \\ \frac{40}{2} + k = 0 \\ 20 + k = 0 \\ \boxed{ \large{k = \underline{ \underline{- 20}}}}$