If x2 + 5kx + 16 = 0, has equal roots, then the value of k is

To find the value of k for which the equation x^2 + 5kx + 16 = 0 has equal roots, we can use the discriminant. The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula b^2 - 4ac.

In this case, a = 1, b = 5k, and c = 16. So the discriminant is (5k)^2 - 4(1)(16) = 25k^2 - 64.

For the equation to have equal roots, the discriminant must be equal to zero. Therefore, we have the equation 25k^2 - 64 = 0.

To solve this equation, we can rearrange it to get 25k^2 = 64 and then divide both sides by 25 to get k^2 = 64/25.

Taking the square root of both sides, we find that k = ±√(64/25).

So the value of k for which the equation has equal roots is k = ±8/5.