Question

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

Answer 1

Given function f(x) = 2x^3+15x^2+22x-15

Leading coefficient is p= 2,and constant q is 15.

If p/q is a rational zero ,then p is a factor of 15 and q is factor of 2.

The possible values of p are ±1,±3,±5

The possible values of q are ±1,±2

By the rational roots theorem,the only possible roots are p/q = ±1, ±1/2, ±3, ±3/2, ±5, ±5/2.

Now we test the each of possibilities.

P(1) = 2+15+22-15 is not equals to 0.

P(-1) = -2+15-22-15 is not equals to 0.

P(2) = 16+60+44-15 is not equals to 0.

P(-2) = -16+60-44-15 is not equals to 0.

P(3) = 54+135+66-15 is not equals to 0.

P(-3)= -54+135-66-15 = 0

P(5) = 250+375+110-15 is not equals to 0.

P(-5) = -250+375-110-15 = 0

P(1/2) = 1/4+15/4+11-15 = 4+11-15 = 0

P(-1/2) = -1/4+15/4-11-15 is not equals to 0.

P(3/2) = 27/4+135/4+33-15 = 163/4+18 is not equals to 0.

P(-3/2) = -27/4+135/4-33-15 = 107/4-48 is not equls to 0.

P(5/2) = 125/4+1875/8+55-15 is not equals to 0.

P(-5/2) = -125/4+1875/8-55-15 is not equls to 0.

Real zeros of the function 2x^3+15x^2+22x-15 is -3,-5,1/2.