Quadratic Equations
Solve for $x$ giving the answer correct to two significant figures: $\;$ $x^2 - 3x - 9 = 0$
Given quadratic equation: $\;$ $x^2 - 3x - 9 = 0$
Comparing with the standard equation $\;$ $ax^2 + bx + c = 0$ gives
$a = 1$, $\;$ $b = - 3$, $\;$ $c = -9$
By quadratic formula, $\;$ $x = \dfrac{- b \pm \sqrt{b^2 - 4a c}}{2 a}$
$\begin{aligned}
i.e. \; \; x & = \dfrac{3 \pm \sqrt{\left(-3\right)^2 - 4 \times 1 \times \left(-9\right)}}{2 \times 1} \\\\
& = \dfrac{3 \pm \sqrt{45}}{2} \\\\
& = \dfrac{3 \pm 6.7082}{2} \\\\
& = \dfrac{9.7082}{2} \; \; or \; \; -\dfrac{3.7082}{2} \\\\
& = 4.8541 \;\; or \; \; -1.8541
\end{aligned}$
i.e. $\;$ $x = 4.9$ $\;$ or $\;$ $x = -1.9$ $\;$ [correct to 2 significant figures]