Quadratic formula questions and answers

Worked solution

1. $b^2 - 4ac = 16 - 4 = 12$
2. $x = \dfrac{-4 \pm \sqrt{12}}{2} = -2 \pm \sqrt{3}$
3. $x = -0.27$ or $x = -3.73$

Worked solution

1. $b^2 - 4ac = 25 - 12 = 13$
2. $x = \dfrac{5 \pm \sqrt{13}}{2}$
3. $x = 4.30$ or $x = 0.70$

Worked solution

1. $b^2 - 4ac = 9 + 32 = 41$
2. $x = \dfrac{-3 \pm \sqrt{41}}{4}$
3. $x = 0.85$ or $x = -2.35$

Worked solution

1. $b^2 - 4ac = 49 - 12 = 37$
2. $x = \dfrac{7 \pm \sqrt{37}}{6}$
3. $x = 2.18$ or $x = 0.15$

Worked solution

1. $b^2 - 4ac = 4 - 20 = -16$
2. It's negative, so there's no real square root and no real solutions.

Worked solution

1. $x = \dfrac{6 \pm \sqrt{36 - 16}}{2} = \dfrac{6 \pm \sqrt{20}}{2}$
2. $\sqrt{20} = 2\sqrt{5}$, so $x = 3 \pm \sqrt{5}$

Worked solution

1. $b^2 - 4ac = 4 + 20 = 24$
2. $x = \dfrac{-2 \pm \sqrt{24}}{10}$
3. $x = 0.29$ or $x = -0.69$

Worked solution

1. $x = \dfrac{-4 \pm \sqrt{16 + 120}}{2} = -2 \pm \sqrt{34}$
2. $x = 3.83$ (the negative solution can't be a width)