Question

If one zero of the quadratic polynomial (k − 1) x² + kx + 1 is −4, then the value of k is

(a) $\frac{-5}{4}$
(b) $\frac{5}{4}$
(c) $\frac{-4}{3}$
(d) $\frac{4}{3}$

Answer 1

$$\begin{gathered} \left(\text{b}\right)\frac{5}{4} \\ \begin{array}{l}\text{Since}-4\text{is a zero of}(k-1)x^2+kx+1,\text{we have:}\\ (k-1)\times {(-4)}^2+k\times (-4)+1=0\end{array} \\ =>16k-16-4k+1=0 \\ =>12k-15=0 \\ =>k=\frac{\sout{1}{\sout{5}}^5}{\sout{1}{\sout{2}}^4} \\ =>k=\frac{5}{4} \end{gathered}$$