Write the Zeros of the Quadratic Polynomial f(x) = 4√3x² + 5x – 2√3
By BYJU'S Exam Prep
Updated on: October 17th, 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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