Question

Obtain other zeros of polynomial 2 x to the power 4 + 3 x cube minus 5 x square - 9 x minus 3 if the zeros root 3 and minus root 3

Answer 1

Step-by-step explanation:

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

   f(1) = 13 − 3×12 – 2×1 + 4 = 0                        1 is a solution

   f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2      

   f(2) = 23 − 3×22 – 2×2 + 4 = −4

   f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

   f(4) = 43 − 3×42 – 2×4 + 4 = 12

   f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.