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4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula?
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4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula?
Using the Quadratic Formula to Solve the Equation:
To solve the equation 4√3x^2 + 5x - 2√3 = 0, we can use the quadratic formula which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / 2a.
Identify the Coefficients:
- In this equation, a = 4√3, b = 5, and c = -2√3.
Substitute into the Quadratic Formula:
- Plugging these values into the formula, we get x = (-(5) ± √((5)^2 - 4*(4√3)*(-2√3))) / 2*(4√3).
Simplify the Expression:
- Simplifying further, x = (-5 ± √(25 + 96)) / 8√3
- x = (-5 ± √121) / 8√3
- x = (-5 ± 11) / 8√3
Calculate the Solutions:
- The two possible solutions are:
- x = (-5 + 11) / 8√3 = 6 / 8√3 = 3 / 4√3 = (3√3) / 4
- x = (-5 - 11) / 8√3 = -16 / 8√3 = -2√3
Therefore, the solutions to the equation 4√3x^2 + 5x - 2√3 = 0 are x = (3√3) / 4 and x = -2√3.
To solve the equation 4√3x^2 + 5x - 2√3 = 0, we can use the quadratic formula which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / 2a.
Identify the Coefficients:
- In this equation, a = 4√3, b = 5, and c = -2√3.
Substitute into the Quadratic Formula:
- Plugging these values into the formula, we get x = (-(5) ± √((5)^2 - 4*(4√3)*(-2√3))) / 2*(4√3).
Simplify the Expression:
- Simplifying further, x = (-5 ± √(25 + 96)) / 8√3
- x = (-5 ± √121) / 8√3
- x = (-5 ± 11) / 8√3
Calculate the Solutions:
- The two possible solutions are:
- x = (-5 + 11) / 8√3 = 6 / 8√3 = 3 / 4√3 = (3√3) / 4
- x = (-5 - 11) / 8√3 = -16 / 8√3 = -2√3
Therefore, the solutions to the equation 4√3x^2 + 5x - 2√3 = 0 are x = (3√3) / 4 and x = -2√3.
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4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula?
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4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula?.
4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4 root 3 x square + 5 x minus 2 root 3 is equal to zero using formula?.
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