Question

1. $x^2 + 5x - 6 = 0$
2. $2x^2 - 4x + 5 = 0$

Explanation:

Step1: Factor quadratic (Q9)

$x^2 + 5x - 6 = (x+6)(x-1) = 0$

Step2: Solve for x (Q9)

Set each factor to 0:
$x+6=0 \implies x=-6$; $x-1=0 \implies x=1$

Step3: Identify coefficients (Q10)

For $2x^2 -4x +5=0$, $a=2$, $b=-4$, $c=5$

Step4: Use quadratic formula (Q10)

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
Substitute values:
$x = \frac{4 \pm \sqrt{(-4)^2-4(2)(5)}}{2(2)} = \frac{4 \pm \sqrt{16-40}}{4} = \frac{4 \pm \sqrt{-24}}{4}$

Step5: Simplify complex roots (Q10)

$\sqrt{-24} = 2i\sqrt{6}$, so:
$x = \frac{4 \pm 2i\sqrt{6}}{4} = \frac{2 \pm i\sqrt{6}}{2}$

Answer:

1. $x = -6$ or $x = 1$
2. $x = \frac{2 + i\sqrt{6}}{2}$ or $x = \frac{2 - i\sqrt{6}}{2}$