Question

If one zero of the polynomial 5x2 +13x+k is reciprocal of the other, then find the value of k

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{One zero of}\;\mathsf{5x^2+13x+k}\;\textsf{is reciprocal of the other}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'k'}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;\alpha\;and\;\dfrac{1}{\alpha}\;be\;the\;zeroes\;of\;the\;polynomial}$

$\mathsf{Then,}$

$\mathsf{Product\;of\;zeroes=\dfrac{c}{a}}$

$\implies\mathsf{\alpha{\times}\dfrac{1}{\alpha}=\dfrac{k}{5}}$

$\implies\mathsf{1=\dfrac{k}{5}}$

$\implies\boxed{\bf\,k=5}$