Question

One root of the quadratic equation 2x^2 − 8x − k =0 is 5/2. Find the other root and the value of k

Answer 1

$p(x) = 2x {}^{2} - 8x - k = 0 \\ p( \frac{5 }{2} ) = 2( \frac{5}{2} ) {}^{2} - 8 \times \frac{5}{2} - k = 0 \\ = 2 \times \frac{25}{4} - 20 - k = 0 \\ = \frac{25}{2} - 20 - k = 0 \\ k = \frac{15}{2 }$