Question

if the quadratic equation kx2- 2kx- 3=0 has equal roots, then find th value of k

Answer 1

Answer:

For k = -3 , the quadratic equation $kx^2-2kx-3=0$ has equal roots.

Step-by-step explanation:

Consider the given quadratic equation $kx^2-2kx-3=0$.

We have to find the value of k for which quadratic equation has equal roots.

A quadratic equation $ax^2+bx+c=0$ has equal roots when discriminant = 0.

That is $\sqrt{b^2-4ac}=0$

Comparing with given quadratic equation, we get, a=k , b = -2k , c = -3 ,

Substitute above, we get,

$\Rightarrow \sqrt{(-2k)^2-4\times k \times (-3)}=0$

$\Rightarrow \sqrt{4k^2+12k}=0$

Taking square both sides, we get,

$\Rightarrow 4k^2+12k=0$

Taking 4k common from both side,

$\Rightarrow 4k(k+3)=0$

$\Rightarrow 4k=0$ or  $\Rightarrow (k+3)=0$

$\Rightarrow k=0$ or  $\Rightarrow k=-3$

Since,  k ≠ 0, as when k =0 then our equation will not be quadratic equation.

Thus, for k = -3 , the quadratic equation $kx^2-2kx-3=0$ has equal roots.

Answer 2

Answer:

Step-by-step explanation:

K = -3

Hope this helps you.