Find the zeros of the following quadratic polynomials 6x2 - 3 - 7x and verify the relationship between the zeros and the coefficients.

By Ritesh|Updated : November 4th, 2022

The zeros of the following quadratic polynomials 6x2 - 3 - 7x are 3/2 and -⅓. Steps to Calculate the zeros of the following quadratic polynomials 6x2 - 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, - ⅓

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 (-⅓) = -3/6 = -½

Again, c/a = -3/6 = -½

As a result, the polynomial's zeroes and coefficients are proven to be related. Consequently, this polynomial's zeros are 3/2 and -⅓

Summary:

Find the zeros of the following quadratic polynomials 6x2 - 3 - 7x and verify the relationship between the zeros and the coefficients.

The quadratic polynomials' 6x2 - 3 - 7x zeros are 3/2 and -⅓. A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable).

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