Question

Find the value (s) of k for which the equation xsquare+5kx+16=0 has real and equal roots

Answer 1

Hey There!!

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${x}^{2} + 5kx + 16$
Since this Equation has real and equal roots,

Therefore,

${b}^{2} \: - \: 4ac \: = 0$
Therefore,

$(5k)^{2} \: - \: 4 \times 1 \times 16 = 0$

=
$25 {k}^{2} \: - 64 = 0$

=
${k}^{2} = \: 64 \div 25$
=
$k \: = \sqrt{\frac{64}{25} }$
=
$k = \frac{8}{5}$
Therefore, K = 8/5

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