# Find the zeros of the quadratic polynomial 6×2 – 3 – 7x and verify the relationship between the zeros and the coefficients.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The zeros of the quadratic polynomial 6x ^ 2 – 3 – 7x are 3/2 and -1/3. Specific formulas can be used to specify the relationship between polynomial zeroes and coefficients depending on the kind of polynomial. We are aware that the quadratic equation has the conventional form ax2 + bx + c = 0. Find the polynomial’s zeros and factorize the quadratic polynomial to make it simpler.

## 6×2-3-7x Find the Zeros

The question states Find the zeros of the quadratic polynomial 6×2 – 3 – 7x and verify the relationship between the zeros and the coefficients. We know that α + β = – b / a and the sum of zeroes = – coefficient of x / coefficient of x2 respectively, thus we can use this to find the sum of zeroes. Additionally, Product of Zeroes = constant term/x2 coefficient, and c / a. where and represent the polynomial’s zeros.

Put the values in the formula above and determine the relationship between the coefficients and zeros. The zeros of the following quadratic polynomial 6x2 – 3 – 7x are 3/2 and -1/3. Candidates are advised to follow the below steps to calculate the zeros of the quadratic polynomial 6x ^ 2 – 3 – 7x.

Step 1: Form the equation

The given polynomial is 6x2 – 3 – 7x.

We are known that a polynomial’s zeroes are evaluated by equating them to zero.

• p (x) = 0
• 6x2 – 3 – 7x = 0

Step 2: Find the zeros by solving the equation.

• 6x2 – 3 – 7x = 0
• 6x2 – 9x + 2x – 3 = 0

On simplifying we get:

• 3x ( 2x – 3) + 1 (2x – 3) = 0
• (2x – 3) (3x + 1) = 0
• x = 3/2, -1/3

Step 3: Verification

We know that for a given polynomial ax2 + bx + c

• Sum of the zeroes = -b/a and product of the roots = c/a
• Sum of the zeroes = 3/2 – ⅓ = (9 – 2)/6 = 7/3

Again, -b/a = – (-7)/ 6 = 7/6

• Product of the zeroes = 3/2 x (-1/3) = -3/6 = -1/2

Again, c/a = -3/6 = -1/2

As a result, the polynomial’s zeroes and coefficients are proven to be related. Consequently, this polynomial’s zeros are 3/2 and -1/3.

Summary:

## Find the zeros of the quadratic polynomial 6×2 – 3 – 7x and verify the relationship between the zeros and the coefficients.

The quadratic polynomial 6x ^ 2 – 3 – 7x zeros are 3/2 and -1/3. A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division. We are aware that the quadratic equation has the typical form: ax2 + bx + c = 0. Find the zeroes of the quadratic polynomial and factor it to make it shorter.

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