Question

If one zero of the quadratic polynomial p(x) = 3x2−8x−2k−13x2−8x−2k−1is seven times the other, then find the value of k.

Answer 1

Dear Student ,

$$\begin{gathered} Solvingyourquestionbytakingequationas \\ p\left(x\right)=3x^2-8x-2k-1 \\ Letonezerobe\alpha \\ then,otherzero=7\alpha \\ Now,sumofzeros,=\frac{-coefficientofx}{coefficientof{x}^2} \\ \alpha +7\alpha =\frac{-\left(-8\right)}{3} \\ 8\alpha =\frac{8}{3} \\ \alpha =\frac{1}{3} \\ Productofzeros=\frac{cons\tan t}{coefficientof{x}^2} \\ \alpha \times 7\alpha =\frac{-\left(2k+1\right)}{3} \\ 7{\alpha }^2\times 3=-\left(2k+1\right) \\ 21{\alpha }^2=-\left(2k+1\right) \\ u\sin gvalueof\alpha \\ 21\times \frac{1}{9}=-\left(2k+1\right) \\ \frac{7}{3}=-\left(2k+1\right) \\ 2k=-1-\frac{7}{3} \\ 2k=\frac{-3-7}{3} \\ k=\frac{-10}{6} \\ \mathit{k}\mathbf{=}\frac{\mathbf{-}\mathbf{5}}{\mathbf{3}} \end{gathered}$$

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