. Find all the zeros of the polynomial 2x4 + 7x3 ? 19x2 ? 14x + 30, if two zeros are root 2 and -root2
Thank you so much
Let us call the polynomial as f (x) just for convenience. As root 2 and -root 2 are two zeroes of f (x) , x^2-2 is a factor of f (x). On dividing f (x) by x^2-2, q (x) will be 2x^2+7x-15 which is also its factor. Factorisation of q (x) will give 3/2 and -5 which are also its zeroes.
Hence the zeroes of f (x) are root2, -root2, -5 and 3/2.