Find the roots of the quadratic equation $x^2 - 3x - 10 = 0$ using the quadratic formula.
Step-by-Step Solution
Key Concept: Quadratic formula $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
Stepwise Solution:
Here $a=1, b=-3, c=-10$. $D = b^2 - 4ac = (-3)^2 - 4(1)(-10) = 9 + 40 = 49$. [1.0 Mark]
$x = \dfrac{-(-3) \pm \sqrt{49}}{2(1)} = \dfrac{3 \pm 7}{2}$.
$x = \dfrac{3 + 7}{2} = 5$ or $x = \dfrac{3 - 7}{2} = -2$. Roots are $5$ and $-2$. [1.0 Mark]
Marking Scheme:
• Calculating $D = 49$: 1.0 Mark
• Applying quadratic formula to find roots $5$ and $-2$: 1.0 Mark
Correct Answer: