Question

if X is equals to - 1 /2 is a solution of equation 3x^2 + 2kx - 3 find k

Answer 1

3x2+2kx−3=03x2+2kx−3=0

Solutions are,

x=−2k±4k2+4∗3∗3√2∗3x=−2k±4k2+4∗3∗32∗3

x=−k±k2+9√3x=−k±k2+93

Since it is given that x=−12x=−12,

−k±k2+9√3=−12−k±k2+93=−12

−k±k2+9‾‾‾‾‾‾√=−32−k±k2+9=−32

k2+9=(k−32)2=k2−3k+94k2+9=(k−32)2=k2−3k+94

3k=94−93k=94−9

k=−94

Answer 2

$3( { \frac{ - 1}{2} })^{2} + 2k( \frac{ - 1}{2} ) - 3 = 0 \\ = > 3 \times \frac{ - 1}{2} \times \frac{ - 1}{2} + 2k \times \frac{ - 1}{2} - 3 = 0 \\ = > \frac{3}{4} - k - 3 = 0 \\ = > - k = 3 - \frac{3}{4 } \\ = > - k = \frac{12 - 3}{4} \\ = > - k = \frac{9}{4} \\ = > k = - \frac{9}{4}$

Hope it helps
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