Question

6a^2x^2 -7abx -3b^2=0 find roots of this quadratic equation using formula.

Answer 1

$x = \frac{3b}{2a} \: \: \: and \: \: \: x = \frac{ - b}{3a}$

Step-by-step explanation:

$Given, \: \: 6a^2x^2 -7abx -3b^2=0 \\ we \: \: know \: \: \boxed{x = \frac{ - B ± \sqrt{ {B}^{2} - 4AC} }{2A}} \\ putting \: \: values \\ x = \frac{ - ( - 7ab)± \sqrt{( - 7ab)^{2} - 4 \times 6 {a}^{2} \times - 3 {b}^{2} } }{2 \times 6 {a}^{2} } \\ = \frac{7ab± \sqrt{49 {a}^{2} {b}^{2} + 72 {a}^{2} {b}^{2} } }{12 {a}^{2} } \\ = \frac{7ab± \sqrt{121 {a}^{2} {b}^{2} } }{12 {a}^{2} } \\ = \frac{7ab±11ab}{12 {a}^{2} } \\ Now, \: \: x = \frac{7ab + 11ab}{12 {a}^{2} } \: \: \: and \: \: \: x = \frac{7ab - 11ab}{12 {a}^{2} } \\ x = \frac{18ab}{12 {a}^{2} } \: \: \: and \: \: \: x = \frac{ - 4ab}{12 {a}^{2} } \\ \boxed{x = \frac{3b}{2a} \: \: \: and \: \: \: x = \frac{ - b}{3a} }$