Question

Determine the value of k, a and b in each of the following quadratic equation, for
which the given value of x is the root of the given quadratic equation :

(i) 6x² + kx - √6 = 0;x = -√3/2​

Answer 1

Step-by-step explanation:

$6 {x}^{2} + kx - \sqrt{6} = 0 \\ given \: x = - \frac{ \sqrt{3} }{2} \\ 6 {( - \frac{ \sqrt{3} }{2} ) \: }^{2} + k( - \frac{ \sqrt{3} }{2} ) - \sqrt{6} \: = 0 \\ 6 \: \: ( \frac{3}{4} ) \: - \frac{ \sqrt{3} \: k }{2} - \sqrt{6} = 0 \\ > > L.C.M \: of \: 2 \: and \: 4 \: is \: 4 < < \\ \frac{18 - 2 \sqrt{3} \: k - 4 \sqrt{6} }{4} = 0 \\ 18 - 2 \sqrt{3} \: k \: - 4 \sqrt{6} = 0 \\ 18 - 4 \sqrt{6} = 2 \sqrt{3} \: k \\ k = \frac{(18 - 4 \sqrt{6} \: ) }{2 \sqrt{3} }$