Coaching Centre
The quadratic formula
Solving any quadratic equation ax² + bx + c = 0 with the quadratic formula, exact surd answers and decimal approximations.
The formula
Quadratic formula
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Solve $x^2 + 5x + 3 = 0$.
$a = 1$, $b = 5$, $c = 3$: $x = \dfrac{-5 \pm \sqrt{25 - 12}}{2}$
$x = \dfrac{-5 \pm \sqrt{13}}{2} \approx -0.70$ or $-4.30$
Solve $2x^2 - 3x - 4 = 0$.
$x = \dfrac{3 \pm \sqrt{9 + 32}}{4} = \dfrac{3 \pm \sqrt{41}}{4}$
$x \approx 2.35$ or $-0.85$
Quadratic formula
$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
First step
Make one side zero.
$x^2 - 2x - 1 = 0$
$x = 1 \pm \sqrt{2}$
Solve $x^2 + 5x + 3 = 0$ (2 d.p.).
$\dfrac{-5 \pm \sqrt{13}}{2}$.
Solve $2x^2 - 3x - 4 = 0$ (2 d.p.).
$\dfrac{3 \pm \sqrt{41}}{4}$.
Exact solutions of $x^2 - 2x - 1 = 0$?
$\dfrac{2 \pm \sqrt{8}}{2}$.
Solve $x^2 - 5x + 6 = 0$ with the formula.
$\dfrac{5 \pm 1}{2}$.
For $x^2 + 5x + 3 = 0$, the value under the square root is?
$25 - 12$.
Solve $2x^2 + 5x - 3 = 0$.
$\dfrac{-5 \pm 7}{4}$.
Solve $x^2 + x - 5 = 0$ (2 d.p.).
$\dfrac{-1 \pm \sqrt{21}}{2}$.
Solve $3x^2 + 4x + 1 = 0$.
$\dfrac{-4 \pm 2}{6}$.
New numbers every time. Keep going until you get five in a row.