The quadratic equation (k+1)x^2 + (5k - 3)x + 3k = 0 has equal roots. Find the possible values of k
We know the discriminant (b^2 - 4ac) must be equal to zero for an equation to have equal roots (think about the fact that the square root of this is taken in the quadratic equation). So we can form the equation (5k-3)^2 - 4(k+1)(3k) = 0Simplifying this to 13k^2 - 42k + 9 = 0 and factorising to (13k - 3)(k - 3) = 0 (easily done by spotting that 13 is prime), we can see that k = 3 or k = 3/13
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