Question

Without solving the quadratic equation find if x = 1 is a root of 3x² − 2x – 1

Answer 1

Step-by-step explanation:

3x²-2x-1=0

3x²-3x+x-1=0

3x(x-1)+1(x-1)=0

x=1,x=-1/3

Answer 2

Given:-

• A quadratic equⁿ is given to us.
• The equⁿ is 3x² - 2x -1 .
• One of its zeroes is 1.

To Find:-

• The other zero.

Answer:-

Here , the quadratic equation is 3x² - 2x -1 = 0.

Since the degree of the polynomial is 2 , it will have two zeroes . And one zero is 1 .

So , if x = 1 , is a zero of polynomial , then ( x - 1 ) will be a factor of the given polynomial .

On dividing we get ,

x - 1 ) 3x² - 2x - 1 ( 3x + 1

3x² - 3x

- +

_______________

x - 1

x - 1

- +

_______________

0

Hence the other factor is 3x + 1 .

Equate this with 0 ,

⇒ 3x + 1 = 0.

⇒ 3x = 0-1.

⇒ 3x = (-1).

➥ 3x = -1/3 .

Hence the other zero is -1/3.