Question

Find other zeroes of the polynomial p(x) = 2x⁴ + 7x³ − 19x² − 14x + 30 if two of its zeroes are $\sqrt{2}$ and $\sqrt{-2}$.

Answer 1

The given polynomial is and two zeroes of this polynomial areand, then we have to find the two other zeroes of

If two zeroes of the polynomial are and, then

is a factor of

Therefore can be written as

The other two zeroes are obtained from the polynomial

Hence the other zeroes are and