Question

If the product of the roots of the equation $x^2-3x+k=10$ is −2, then the value of k is
(a) −2
(b) −8
(c) 8
(d) 12

Answer 1

(c) 8
$$\begin{gathered} \text{It is given that the product of the roots of the equation}{x}^2-3x+k=10\text{is}-2. \\ \mathrm{The}\mathrm{equation}\mathrm{can}\mathrm{be}\mathrm{rewritten}\mathrm{as}: \\ {x}^2-3x+(k-10)=0 \\ \mathrm{Product\; of\; the\; roots\; of}\mathrm{a}\mathrm{quadratic}equation=\frac{c}{a} \\ \Rightarrow \frac{c}{a}=-2 \\ \Rightarrow \frac{(k-10)}{1}=-2 \\ \Rightarrow k=8 \end{gathered}$$