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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
Answer:
Therefore, solutions to the quadratic equation √3x² – 8x + 4√3 = 0 are x = (2√3) / 3 and x = 2√3.
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