Question

the solutions of the equation are

Answer 1

★ Given :

Equation : y² - 3y - 9 = 0

★ To Find :

We have to find the solutions of the equation y² - 3y - 9 = 0

★ Explanation :

We will do this question by Discriminant method because there are no real roots of the equation.

So, A.T.Q

$\large{\star{\underline{\boxed{\sf{y = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} }}}}} \\ \\ \sf{\dashrightarrow y = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-9)}}{2(1)}} \\ \\ \sf{\dashrightarrow y = \dfrac{3 \pm \sqrt{9 + 36}}{2}} \\ \\ \sf{\dashrightarrow y = \dfrac{3 \pm \sqrt{45}}{2}} \\ \\ \sf{\dashrightarrow y = \dfrac{3 \pm \sqrt{3 \times 3 \times 5}}{2}} \\ \\ \sf{\dashrightarrow y = \dfrac{3 \pm 3\sqrt{5}}{2}} \\ \\ \Large{\star{\underline{\boxed{\sf{ \dfrac{3 \pm 3\sqrt{5}}{2} }}}}}\\ \\ \bf{\therefore \: Option \: 4 \: is \: correct.}$