Question

The roots of a quadratic equation 9x 15x + 6 =0 are: a) 1/4 and-1/4 b) 1/2 and-1/2 c) 1/2 and 3/2 d) 1/2 and 2​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The given equation is }9x^{2} + 15x + 6 = 0$

       $\text{Taking 3 common}$

$\implies 3(3x^{2} + 5x + 2) = 0$

$\implies 3x^{2} + 5x + 2 = 0$

       $\text{We can split }5x \text{ as }(3x+2x)$

$\implies 3x^{2} + 3x + 2x + 2 = 0$

$\implies 3x(x+ 1) + 2(x+1) = 0$

$\implies (x+1)(3x+2) = 0$

$\implies \boxed{x = -1, -\dfrac{3}{2}}$