Question

if the equation 16x2+6kx+4=0 has equal root then what is the value of k

Answer 1

$\textsf{Given equation is }\mathsf{16x^2+6kx+4=0}$

$\textsf{Here, a=16,\;\;b=6k,\;\;c=4}$

$\textsf{Condition for equal roots is }\mathsf{b^2-4ac=0}$

$\implies\mathsf{(6k)^2-4{\times}16{\times}4=0}$

$\implies\mathsf{(6k)^2-16^2=0}$

$\implies\mathsf{(6k+16)(6k-16)=0}$

$\implies\mathsf{6k=16,-16}$

$\implies\mathsf{k=\frac{16}{6},\frac{-16}{6}}$

$\implies\mathsf{k=\frac{8}{3},\frac{-8}{3}}$

$\therefore\textsf{The value of k is }\mathsf{k=\frac{8}{3},\frac{-8}{3}}$

Answer 2

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