# Find the Zeros of the Quadratic Polynomial √3x² – 8x + 4√3.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Find the zeros of the quadratic polynomial √3x² – 8x + 4√3.

We can find the zeroes of the polynomial √3x² – 8x + 4√3 by factoriozation.

To find the zeros of a quadratic polynomial by factorization, you can follow these steps:

• Write the quadratic polynomial in standard form: ax² + bx + c, where a, b, and c are constants.
• Factor the quadratic expression, if possible, by finding two binomials that multiply to give the quadratic expression.
• Check your solutions by plugging them back into the original equation. If both solutions make the equation true, then they are valid solutions.

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## Solution:

√3x² – 8x + 4√3 = 0 can be factorized as:

√3x² – 6x – 2x + 4√3 = 0

(√3x – 2)(x – 2√3) = 0

Therefore, the solutions to the quadratic equation are:

√3x – 2 = 0 or x – 2√3 = 0

√3x = 2 or x = 2√3

Dividing both sides of the equation √3x = 2 by √3, we get:

x = 2/√3 = (2√3) / 3