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Chapter 7: Q. 1 (page 505)

Find the real solutions, if any, of the equation3x2+x-1=0.

Short Answer

Expert verified

The solutions are-1-136,-1+136.

Step by step solution

01

Step 1. Given Information

We are given the equation3x2+x-1=0and we need to find the real roots of it.

02

Step 2. Finding the discriminant

The standard form of a quadratic equation is ax2+bx+c=0.

Comparing it with the given equation we get,

a=3,b=1,c=-1.

Discriminant of the equation is

role="math" localid="1646502307564" b2-4ac=(1)2-4(3)(-1)=1+12=13>0

Thus there are two unequal real solutions forx.

03

Step 3. Finding the roots

Using the quadratic formula to find the roots:

x=-b卤b2-4ac2a

Substituting the values we get,

role="math" localid="1646502325187" x=-1卤12-43-123鈬�x=-1卤1+126鈬�x=-1卤136鈬�x=-1-136,-1+136

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