Question

FIND ALL REAL ZEROES OF THE FUNCTION F(X)=2X^3+15X^2+22X-15

Answer 1

First look for rational zeroes. If they exist they could be factors of ±15. Start with -3:

-54+135-66-15=0, so x+3 is a factor. Use synthetic division to find more zeroes:

-3 | 2 15  22 -15

      2 -6 -27 | 15

      2  9   -5 |   0 = 2x²+9x-5=(2x-1)(x+5)

The zeroes of the quadratic are: x=½ and -5. The three zeroes are -5, -3, ½.