The number of non-negative integer values of k for which the quadratic equation $$x^{2}-5x+k=0$$ has only inte

Question

The number of non-negative integer values of k for which the quadratic equation $$x^{2}-5x+k=0$$ has only integer roots, is

Accepted Answer

The given quadratic equation is x 2 − 5 x + k = 0 x^2-5x+k=0 x 2 − 5 x + k = 0 Now, discriminant D = 5 2 − 4 k = 25 − 4 k D=5^2-4k=25-4k D = 5 2 − 4 k = 25 − 4 k Now, it is given the equation must have integer roots. So, 25 − 4 k 25-4k 25 − 4 k has to be a perfect square. We need to find non-negativ

The number of non-negative integer values of k for which the quadratic equation x2−5x+k=0x^{2}-5x+k=0x2−5x+k=0 has only integer roots, is

The number of non-negative integer values of k for which the quadratic equation $x^{2}-5x+k=0$ has only integer roots, is