# Write the Zeros of the Polynomial x²-x-6

By BYJU'S Exam Prep

Updated on: October 17th, 2023

Write the zeros of the polynomial x²-x-6

Check out the steps to systematically find out the zeros of the given polynomial.

Here, we will use the factorization of the middle term:

Step 1: Find two numbers that multiply to -6(multiplication of coefficient of first and the last term) and add up to -1 (the coefficient of the x term). The numbers -3 and 2 satisfy this condition since -3× 2 = -6 and -3 + 2 = -1.

Step 2: Substitute these numbers into the factored form: x² – x – 6 = (x – 3)(x + 2)

Step 3: Write the polynomial in the form of (x – a)(x – b), where a and b are the zeros: x² – x – 6 = (x – a)(x – b)

## Write the Zeros of the Polynomial x²-x-6

Solution:

To find the zeros, we set the polynomial equal to zero:

x² – x – 6 = 0

Next, we can factor the quadratic equation:

(x – 3)(x + 2) = 0

Now, we can set each factor equal to zero:

x – 3 = 0 or x + 2 = 0

Solving these equations, we find the values of x:

x = 3 or x = -2

Therefore, the zeros of the polynomial x² – x – 6 are x = 3 and x = -2.