Question

Find the quadratic equation 2 x square - 7 x + 6 is equal to zero using factorization method

Answer 1

$= {2x}^{2} - 7x + 6 \\ = {2x}^{2} - (4 - 3)x + 6 \\ = {2x}^{2} - 4x - 3x + 6 \\ = 2x(x - 2) - 3(x - 2) \\ = (x - 2)(2x - 3) \\ \\ putting \: (x - 2) \: in \: eq. \\ x - 2 = 0 \\ x = 2 \\ \\ = 2 {(2)}^{2} - 7(2) + 6 \\ = 8 - 14 + 6 \\ = 14 - 14 = 0 \\ \\ putting \: (2x - 3) \\ 2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} \\ \\ = 2 {( \frac{3}{2} )}^{2} - 7( \frac{3}{2}) + 6 \\ = 2 \times \frac{9}{4} - 7 \times \frac{3}{2} + 6 \\ = \frac{9}{2} - \frac{21}{2} + 6 \\ = \frac{9 - 21}{2} + 6 \\ = - \frac{12}{2} + 6 \\ = - 6 + 6 = 0$