   Chapter 0.5, Problem 20E

Chapter
Section
Textbook Problem

By any method, determine all possible real solutions of each equation in Exercises 13–30. Check your answers by substitution. 2 x 2 − x − 3 = 0

To determine

To calculate: The all real solutions in the quadratic equation 2x2x3=0.

Explanation

Given Information:

The provided quadratic equation is 2x2x3=0.

Formula used:

The value of x in the equation ax2+bx+c=0 can be given by the quadratic formula,

x=b±b24ac2a where a,b and c are real numbers with a0.

Calculation:

Consider the quadratic equation 2x2x3=0.

Compare the above equation with the equation ax2+bx+c=0,

a=2, b=1 and c=3

Put the values of a,b,c in the quadratic formula x=b±b24ac2a.

x=(1)±(1)242(3)22=1±1+244=1±254=1±54

Further simplify,

x=1+54=64=32

Or

x=154=44=1

Check:

For x=32

Substitute the value of x=32 in 2x2x3=0

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