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)
Table of content
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.
Answer:
The Zeros of the Polynomial x²-x-6 are 3 and -2.
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