How many real roots does the polynomial 2x^3 8x-7 have?

One. And you don't need to calculate them to know that. First, you know that polynomials of grade three have either one or three real roots. Second, you know that to have three real roots, they have to have a local maximum and a local minimum. read more

Since any complex roots are in complex conjugate pairs, and it has an odd order, it must have at least 1 real root. At -1 it is at -9, at 0 it is at 2, so it has a zero between -1 an 0. The derivative is 4x^4 + 21x^2 + 3 which is always positive. read more

Thereafter the 4 roots are complex. 2) The multiplicity of a root is the number of times that the corresponding factor appears in the polynomial. In this case the factor x + 1 appears two times, then - 1 has multiplicity 2. read more