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Find the roots of the quadratic equation 6x2 – x – 2 = 0. |
Answer» We have 6x2 – x – 2 = 6x2 + 3x – 4x – 2 = 3x (2x + 1) – 2 (2x + 1) = (3x – 2)(2x + 1) The roots of 6x2 – x – 2 = 0 are the values of x for which (3x – 2)(2x + 1) = 0 Therefore, 3x – 2 = 0 or 2x + 1 = 0, i.e., x =2/3 or x =-1/2 Therefore, the roots of 6x2 – x – 2 = 0 are 2/3 and -1/2. We verify the roots, by checking that 2/3 and -1/2 satisfy 6x2 – x – 2 = 0. |
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