Write the Zeros of the Quadratic Polynomial f(x) = 4√3x² + 5x - 2√3

By Mohit Uniyal|Updated : May 12th, 2023

Question: Write the zeros of the quadratic polynomial f(x)=4√3²+5x−2√3.

To find the solution of the quadratic polynomial, we will use the quadratic formula.

The quadratic formula is used to find the solutions, or zeros, of a quadratic equation of the form:

ax² + bx + c = 0

To use the quadratic formula, we need to identify the values of a, b, and c in the quadratic equation. Once we have identified these values, we can substitute them into the quadratic formula:

x = [-b ± √(b²- 4ac)] / 2a

where x represents the solutions of the quadratic equation.

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Solution

Given: f(x) = 4√3x² + 5x - 2√3 = 0

To find the zeros of the quadratic equation, we can use the quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

where a = 4√3, b = 5, and c = -2√3

Plugging in the values, we get:

x = [-5 ± √(5² - 4(4√3)(-2√3))] / 2(4√3)

Simplifying, we get:

x = [-5 ± √(25 + 96)] / (8√3)

x = [-5 ± √121] / (8√3)

x = (-5 ± 11) / (8√3)

So, the solutions are:

x = (-5 + 11) / (8√3) = 6 / (8√3) = √3/4

x = (-5 - 11) / (8√3) = -16 / (8√3) = -2/√3

Answer

The zeros of the quadratic polynomial f(x) are x = -2/√3 and x = √3/4.

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Write the Zeros of the Quadratic Polynomial f(x) = 4√3x² + 5x - 2√3

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