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Chapter 11: Q. 3 (page 796)

In Problems 1-6, solve each equation.

2x3-3x2-8x-3=0.

Short Answer

Expert verified

The solutions for the equation 2x3-3x2-8x-3=0are,x=-1,-12,3.

Step by step solution

01

Step 1 Given equation is,

2x3-3x2-8x-3=0.

The given equation can be solved by assuming a value for xwhich is a solution of the given cubic equation in x.

Substitute x=-1in the given equation.

2-13-3-12-8-1-3=0-2-3+8-3=0-5+5=00=0

Since0=0is a true statement, the valuex=-1is a solution to the given equation.

02

Step 2 The given cubic equation is a product of x+1 and a quadratic equation in x.

2x3-3x2-8x-3=x+1ax2+bx+c.

The quadratic equation can be obtained by dividing the cubic equation by x+1.

03

Step 3 The obtained equation can now be solved by using the formula.

x=5卤-52-42-322=5卤74=-12,3

Hence the required solution set is,-1,-12,3.

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