For ax2+bx+c=0, a 0: x= -b+-sqrt(b2-4ac)2a Solving a quadratic **Method** | **Key step** | **Example** Factorisation | Express as (x-p)(x-q)=0; each factor gives a root. | 2x2+x-6=0 (2x-3)(x+2)=0 x= 32, x=-2 Completing the square | Write the equation as (x+h)2=k, then square-root both sides. | x2+6x+1=0 (x+3)2=8 x=-3+- 2sqrt(2) Quadratic formula | x= -b+-sqrt(b2-4ac)2a | 3x2+2x-2=0 x= -2+-sqrt(28)6 x= -1+- 73 Write the equation with zero on one side before identifying a,b,c.

Express as \((x-p)(x-q)=0\); each factor gives a root.

\(\begin{aligned} 2x^2+x-6&=0 \\ (2x-3)(x+2)&=0 \\ x&=\dfrac{3}{2},\ x=-2 \end{aligned}\)

Write the equation as \((x+h)^2=k\), then square-root both sides.

\(\begin{aligned} x^2+6x+1&=0 \\ (x+3)^2&=8 \\ x&=-3\pm 2\sqrt{2} \end{aligned}\)

\(\begin{aligned} 3x^2+2x-2&=0 \\ x&=\dfrac{-2\pm\sqrt{28}}{6} \\ x&=\dfrac{-1\pm\sqrt7}{3} \end{aligned}\)

Write the equation with zero on one side before identifying \(a,b,c\).

Roots

Roots