Question

If one root of the equation x2

+kx – 12 = 0 is 2 , find the other root.​

Answer 1

As one root is 2 ,other root should be -6 coz the constant term is -12
And so the value of k will be -4
Or
(x-a)*(x-2)= x^2-2x-ax+2a=x^2+kx-12
Now compare
U will get the same answer

Answer 2

$p(x) = x^{2} + kx - 12 \\ since \: one \: zero \: is \: 2 \\ hence \: p(2) = 2 ^{2} + 2k - 12 = 0 \\ 4 - 12 + 2k = 0 \\ - 8 + 2k = 0 \\ 2k = 8 \\ k = \frac{8}{2} \\ k = 4$

$x ^{2} + 4x - 12 = 0 \\ x^{2} + 6x - 2x - 12 = 0 \\ x(x + 6) - 2(x + 6) = 0 \\ (x + 6)(x - 2) = 0$

therefore, x= -6, 2

So the other root is -6