# Find the Zeros of the Quadratic Polynomial x² + 7x + 12 and Verify the Relationship Between the Zeros and the Coefficients

By BYJU'S Exam Prep

Updated on: October 17th, 2023

Find the zeros of the quadratic polynomial x² + 7x + 12 and verify the relationship between the zeros and the coefficients.

To solve the given problem, we will find out the zeros of the polynomial x² + 7x + 12 and then verify the result using the given steps:

• Step 1: Identify the coefficients of the quadratic polynomial.
• Step 2: Factorize to find the zeros of the polynomial.
• Step 3: Verify the relationship between the zeros and the coefficients using Vieta’s formulas.

## Find the Zeros of the Quadratic Polynomial x² + 7x + 12 and Verify the Relationship Between the Zeros and the Coefficients

Solution:

To find the zeros of the quadratic polynomial x²+7x+12, we need to factorize the polynomial or use the quadratic formula.

Let’s factorize it:

x²+7x+12=(x+3)(x+4)

Setting each factor equal to zero, we get:

x+3 = 0 and x+4 = 0

Solving for x in each equation, we find: x=-3 and x=-4

Therefore, the zeros of the quadratic polynomial x²+7x+12 are -3 and -4. Now, let’s verify the relationship between the zeros and the coefficients. For a quadratic polynomial of the form ax²+bx+c, the relationship between the zeros (x1 and x2) and the coefficients is given by Vieta’s formulas:

Sum of the zeros: x1+x2=-b/a

Product of the zeros: x1.x2=c/a

In this case, a=1, b=7, c=12, x1=-3, and x2=-4

Sum of the zeros: (-3)+(-4) = -7 = -7/1 = -b/a

Product of the zeros: (-3)⋅(-4) = 12 = 12/1 = c/a

Both relationships hold true, verifying the relationship between the zeros and the coefficients of the quadratic polynomial x²+7x+12.