Question

if the quadratic equation 2x^2+ kx + 3 = 0 has the equal roots. Then the value of k is -----​

Answer 1

$\sf Let\:the\:root\:of\:quadratic\:equation \\2x^2+ kx + 3 = 0\: be\: \alpha \\\\\sf Now,\:SUM\:of \:roots = \alpha+\alpha = 2\alpha\\=\frac{-b}{a}\\= 2\alpha=\frac{-k}{2} \\= \alpha=\frac{-k}{4} \\\sf Now,\:product\: of\:roots\:=(\alpha)^2= \frac{c}{a}\\=\alpha^2= \frac{3}{2}\\=\alpha= \sqrt{\frac{3}{2}} \\\\\sf Now, \alpha =\frac{-k}{4} =\sqrt{\frac{3}{2}} \\= -k={\frac{4\sqrt{3}}{\sqrt{2}}}\\\sf After, Rationalising, \\= -k ={\frac{4\sqrt{3}}{\sqrt{2}}}\sf{x} \frac{\sqrt{2}}{\sqrt{2} } \\\\= -k =2\sqrt{6}= k=-2\sqrt{6}$