What are the roots of the quadratic equation 21x2 - 37x - 28 = 0?
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What are the roots of the quadratic equation 21x2 - 37x - 28 = 0?
-7/3, 4/7
3/7, -7/4
7/3, -4/7
-3/7, 7/4
21x^2 - 37x - 28 = 0. Using the quadratic formula: x = (37 +/- sqrt(37^2 - 4*21*(-28))) / 42 = (37 +/- sqrt(1369 + 2352)) / 42 = (37 +/- sqrt(3721)) / 42 = (37 +/- 61) / 42. Roots are 98/42 = 7/3 and -24/42 = -4/7.
Using the method of splitting the middle term, we rewrite the quadratic equation 21x^2 - 37x - 28 = 0 as 21x^2 - 49x + 12x - 28 = 0. Factoring by grouping gives 7x(3x - 7) + 4(3x - 7) = 0, which leads to (3x - 7)(7x + 4) = 0. Equating each factor to zero provides the roots x = 7/3 and x = -4/7.