Solving Quadratics by Factorising Flashcards

All 6 cards in this deck

If $(x+a)(x+b)=0$, what can you say?

e.g. $(x+2)(x-7)=0$

One bracket must equal $0$: $x=-a$ or $x=-b$.

e.g. $x=-2$ or $x=7$

What are the steps to solve a quadratic equation by factorising when $a=1$?

e.g. solve $x^2+5x+6=0$

1. Find two numbers with product $c$ and sum $b$: $2$ and $3$
2. Write the brackets: $(x+2)(x+3)=0$
3. Set each bracket to $0$: $x=-2$ or $x=-3$

What are the steps to solve a quadratic equation by factorising when $a\neq1$?

e.g. solve $2x^2+7x+3=0$

1. Find two numbers with product $ac=6$ and sum $b=7$: $6$ and $1$
2. Factorise into two brackets: $(2x+1)(x+3)=0$
3. Set each bracket to $0$: $x=-\frac{1}{2}$ or $x=-3$

What must you do before factorising to solve $x^2=5x+24$?

Rearrange into the form $ax^2+bx+c=0$: $x^2-5x-24=0$

True or false? The solutions of $(3k-2)(k+4)=0$ are $k=2$ and $k=-4$.

False. $3k-2=0$ gives $k=\frac{2}{3}$, so the solutions are $k=\frac{2}{3}$ and $k=-4$.

True or false? To solve $x^2=5x$ you can divide both sides by $x$ to get $x=5$.

False. Dividing by $x$ loses the solution $x=0$; factorise instead: $x(x-5)=0$, so $x=0$ or $x=5$.