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Using the splitting method, find the roots of $12 x^{2} + 7 x - 10 = 0$ .

Class 10Solving by FactorisationQuadratic Equations

A $x = \frac{2}{3}, - \frac{5}{4}$
B $x = - \frac{2}{3}, \frac{5}{4}$
C $x = \frac{3}{2}, - \frac{4}{5}$
D $x = \frac{5}{3}, - \frac{2}{4}$

Step-by-Step Solution

Product

12 * (- 10) = - 120

, sum 7, split 15 and -8.

12 x^{2} + 15 x - 8 x - 10 = 3 x (4 x + 5) - 2 (4 x + 5) = (4 x + 5) (3 x - 2) = 0. x = - \frac{5}{4}

or

x = \frac{2}{3}

.

Answer: A)

x = \frac{2}{3}, - \frac{5}{4}

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