# Find the Zeros of the Following Quadratic Polynomials x²+7x+10 and Verify the Relationship between the Zeros and the Coefficients

By Mohit Uniyal|Updated : May 17th, 2023

Find the zeros of the following quadratic polynomials x²+7x+10 and verify the relationship between the zeros and the coefficients.

To solve this problem, we will use the quadratic formula. For this we will have to identify the coefficients, i.e., a = 1, b = 7, c = 10 and put in x = (-b ± √(b² - 4ac)) / (2a)

On simplifying, we will get the two different zeros of the polynomial which can be again verified with the help of Vieta's formula.

## Find the Zeros of the Following Quadratic Polynomials x²+7x+10 and Verify the Relationship between the Zeros and the Coefficients

Solution:

To find the zeros of the quadratic polynomial x² + 7x + 10, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing the polynomial to the standard quadratic form ax² + bx + c, we have a = 1, b = 7, and c = 10. Substituting these values into the quadratic formula, we get:

x = (-(7) ± √((7)² - 4(1)(10))) / (2(1))

Simplifying further:

x = (-7 ± √(49 - 40)) / 2

x = (-7 ± √9) / 2

x = (-7 ± 3) / 2 = -2

This gives us two possible solutions:

x1 = (-7 + 3) / 2 = -2

x2 = (-7 - 3) / 2 = -5

Therefore, the zeros of the quadratic polynomial x² + 7x + 10 are x = -2 and x = -5.

Now, let's verify the relationship between the zeros and the coefficients using Vieta's formulas:

The sum of the zeros is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term:

Sum of zeros = -(7/1) / (1/1) = -7

The product of the zeros is equal to the constant term divided by the coefficient of the quadratic term:

Product of zeros = (10/1) / (1/1) = 10

Indeed, the sum of the zeros, -7, matches the coefficient of the linear term, and the product of the zeros, 10, matches the constant term. Therefore, the relationship between the zeros and the coefficients is verified. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com