The quadratic formula

Algebra

(1MA1) · Higher

ORIGINAL

When it won't factorise, use the formula — carefully with the signs and the rounding.

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Question

Solve

3x^2 - 5x - 1 = 0

, giving your answers to 2 decimal places.

Every step worked, with the reasoning.

1
$a = 3,\ b = -5,\ c = -1$
Read off the coefficients, keeping the signs.
2
$x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-1)}}{2(3)}$
Substitute into $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
3
$x = \dfrac{5 \pm \sqrt{25 + 12}}{6} = \dfrac{5 \pm \sqrt{37}}{6}$
Simplify: $b^2 - 4ac = 25 - (-12) = 37$ .
4
$x = \dfrac{5 + 6.083}{6}$ or $x = \dfrac{5 - 6.083}{6}$
$\sqrt{37} \approx 6.083$ .
5
$x = 1.85$ or $x = -0.18$ (2 d.p.)
Evaluate each and round to 2 decimal places.

Answer: $x = 1.85$ or $x = -0.18$

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