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Solve quadratic equation by factorization method √3xsquare -2√2x-2√3=0?
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Solve quadratic equation by factorization method √3xsquare -2√2x-2√3=0...
Solving Quadratic Equation by Factorization Method
To solve the quadratic equation √3xsquare -2√2x-2√3=0 by factorization method, we need to follow the steps given below:
Step 1: Identify the values of a, b and c from the given equation, where ax2 + bx + c = 0.
In this equation, a = √3, b = -2√2 and c = -2√3.
Step 2: Multiply 'a' and 'c' and find two factors whose sum is 'b'.
a*c = (√3) × (-2√3) = -6
Factors of -6 whose sum is -2√2 are -3√2 and 2√2.
Step 3: Use the factors obtained in step 2 to rewrite the middle term.
-2√2x = -3√2x + 2√2x
Step 4: Factor the quadratic equation by grouping.
√3x(√3x - 3√2) + 2√2(√3x - 3√2) = 0
(√3x - 3√2)(√3x + 2√2) = 0
Step 5: Set each factor equal to zero and solve for x.
√3x - 3√2 = 0 or √3x + 2√2 = 0
x = 3/√3 or x = -2√2/√3
Step 6: Simplify the solutions.
x = 3√3 or x = -2√6
Therefore, the solutions to the quadratic equation √3xsquare -2√2x-2√3=0 are x = 3√3 or x = -2√6.
To solve the quadratic equation √3xsquare -2√2x-2√3=0 by factorization method, we need to follow the steps given below:
Step 1: Identify the values of a, b and c from the given equation, where ax2 + bx + c = 0.
In this equation, a = √3, b = -2√2 and c = -2√3.
Step 2: Multiply 'a' and 'c' and find two factors whose sum is 'b'.
a*c = (√3) × (-2√3) = -6
Factors of -6 whose sum is -2√2 are -3√2 and 2√2.
Step 3: Use the factors obtained in step 2 to rewrite the middle term.
-2√2x = -3√2x + 2√2x
Step 4: Factor the quadratic equation by grouping.
√3x(√3x - 3√2) + 2√2(√3x - 3√2) = 0
(√3x - 3√2)(√3x + 2√2) = 0
Step 5: Set each factor equal to zero and solve for x.
√3x - 3√2 = 0 or √3x + 2√2 = 0
x = 3/√3 or x = -2√2/√3
Step 6: Simplify the solutions.
x = 3√3 or x = -2√6
Therefore, the solutions to the quadratic equation √3xsquare -2√2x-2√3=0 are x = 3√3 or x = -2√6.
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Solve quadratic equation by factorization method √3xsquare -2√2x-2√3=0...
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Solve quadratic equation by factorization method √3xsquare -2√2x-2√3=0?
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