Question

which of the following are the roots of 3xsquare + 2x - 1 = 0

Answer 1

Answer :–

• –1 and $\sf \frac{1}{3}$ are the required roots for the given polynomial.

Given :–

• A quadratic polynomial = 3x² + 2x – 1.

To Find :–

• Roots of the given polynomial.

Solution :–

First we need to factorise the given quadratic polynomial,

So,

→ 3x² + 2x – 1

→ 3x² + 3x – x – 1

→ 3x(x + 1) – 1(x + 1)

→ (x + 1)(3x – 1)

So, the factors of this quadratic polynomial is (x + 1)(3x – 1).

Now, we have to find the roots of this polynomial.

For finding the roots of the polynomial,

Put, 3x² + 2x – 1 = 0

Put, the factors of this given quadratic polynomial,

1. x + 1

→ x + 1 = 0

→ x = –1

2. 3x – 1

→ 3x – 1 = 0

→ 3x = 1

→ x = $\sf \frac{1}{3}$

Hence,

–1 and $\sf \frac{1}{3}$ are the required roots for the given polynomial.

Answer 2

$\large \underline{ \sf{ANSWER :}}$

x = 1/3 and x = -1

$\large \underline{ \sf{ SOLUTION :}}$

Given ,

The polynomial is 3(x)² + 2x - 1 = 0

By prime factorisation method , we get

3(x)² + 3x - 1x - 1 = 0

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

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

x = 1/3 or x = -1

Therefore ,

• The roots of given polynomial are 1/3 and -1