Question

find the values of k for which of the following equations have equal roots (k-12)x²+2(k-12)x+2=0​

Answer 1

Answer:

12+2$\sqrt{6}$, 12-2$\sqrt{6}$

Step-by-step explanation:

For a quadratic equation to have equal roots , the discriminant =0

i.e. b^2- 4ac= 0;

In the given equation b= 2(k-12), a= 12 , c=2;

now D=0

$b^{2}$- 4ac=0;

upon solving the above equation you get a quadratic equation in terms ok k

which is $k^{2}$-24k+120=0;

now use the direct formula of finding roots of a equation

x=( -b + $\sqrt{b^2-4ac}$)/2a      ;     (-b - $\sqrt{b^2-4ac}$)/2a