Solving Quadratic Equations (Edexcel IGCSE Maths): Exam Questions

Solve $( x - 2 )^{2 } = 3$

Give your solutions correct to $3$ significant figures.

Solve the equation $3x^{2}+4x-12=0$

Give your solutions correct to $2$ decimal places.

Solve $3x^{2}+6x-2=0$

Give your solutions correct to $2$decimal places.

Solve $3x^{2}-x-1=0$

Give your solutions correct to $2$ decimal places.

Solve $x^{2}-5x+3=0$

Give your solutions correct to $3$ significant figures.

Liz is asked to solve the equation $3x^{2}+8=83$

Here is her working.

$\begin{gathered} 3 x^{2} + 8 & = 83 \\ 3 x^{2} & = 75 \\ x^{2 } & = 25 \\ x & = 5 \end{gathered}$

Explain what is wrong with Liz's answer.

Solve $3x^{2}-4x-2=0$

Give your solutions correct to $3$ significant figures.

Solve $3x^{2}-5x-1=0$

Give your solutions correct to $3$ significant figures.

Solve $2x^{2}+3x-7=0$

Give your solutions correct to $2$ decimal places.

Factorise $x^{2}+2x--24$.

Hence solve $x^{2}+2x--24=0$

Solve $x^{2}--21x+20=0$

Show your working clearly.

The only solution to $x^{2}+bx+c=0$ is $x=5$

Work out the values of $b$ and $c$.

$b=....................\,c=.....................$

Write $x(3x--9)=4$ in the form $ax^{2}+bx+c=0$ where $a,b$ and $c$are integers.

Solve$x(3x--9)=4$

Give your answers to 2 decimal places.

Solve $x^{2}-x-12=0$

Without expanding any brackets,

show how to work out the exact solutions of $9(x+3)^{2}=4$

Give the solutions.

Solve by factorising.

$x^{2}+9x+20=0$

$x$= ....................... or $x$ = .......................

Solve this equation algebraically. Give your solutions correct to 2 decimal places.

3x² + 8x - 5 = 0

x = .................... or x = ....................

Solve.

$x^{2}-6x+15=3x-5$

$x=$.............. or $x=$..............

Solve.

$3x^{2}=75$

$x$ = .................

(i) Factorise $x^{2}+9x--22$

(ii) Hence solve $x^{2}+9x--22=0$

Solve $x^{2}-6x-8=0$

Write your answer in the form $a\pm\sqrt{b}$ where $a$and $b$are integers.

Alison is using the quadratic formula to solve a quadratic equation.

She substitutes values into the formula and correctly gets.

$x=\frac{-7\pm\sqrt{49-32}}{4}$

Work out the quadratic equation that Alison is solving.

Give your answer in the form $ax^{2}+bx+c=0$, where $a,b$ and $c$ are integers.

The area of square $ABCD$ is $10$ cm². Show that $x^{2}+6x=1$

Solve $5x^{2}=10x+4$

Give your answers to 2 decimal places.

$2x^{2}-6x+5$ can be written in the form $a(x-b)^{2}+c$

where $a,b$ and$c$ are positive numbers. Work out the values of $a,b$ and $c$.

$\begin{array}{rcl} a = ................... \\ b = ................... \\ c = ................... \end{array}$

Using your answer to part (a), or otherwise, solve $2x^{2}--6x+5=8.5$

Here are two pieces of work.

For each one, describe the error made and give the complete correct solution.

Error: ........................................................ Correct solution:

Error: ..................................................................... Correct solution:

Solve by factorisation.

$5x^{2}+7x+2=0$

x = ............................ or* x *= ............................

Solve by factorisation.

2x² − 19x − 33 = 0

x = ................... or x = ..................

(i) Write $x^{2}+4x-16$ in the form $( x + a )^{2} - b$.

(ii) Solve the equation $x^{2}+4x-16=0$.

Give your answers in surd form as simply as possible.

$x$ = ........... or $x$ = .......... [4]

Solve by factorisation $10r^{2}-23r+9=0$.

$r$ = ................... or $r$ = ...................

Solve $x^{2} = 4 ( x - 3 )^{2}$

Solve $2x^{2}+9x-7=0$

Give your solutions correct to $3$ significant figures.

Solve $\frac{2}{y^{2}}+\frac{9}{y}-7=0$

Give your solutions correct to $3$ significant figures.

Given that

$2x-1:x-4=16x+1:2x-1$

find the possible values of $x$.

The diagram shows a trapezium.

All the measurements are in centimetres.

The area of the trapezium is $351$ cm².

Show that $2x^{2}+x-351=0$

Work out the value of $x$.

Given that

$x^{2} : ( 3 x + 5 ) = 1 : 2$

find the possible values of $x$.

The lengths of the sides are in centimetres.

The area of triangle T₁ is equal to the area of triangle T₂.

Work out the value of $x$, giving your answer in the form $a+\sqrt{b}$ where $a$ and $b$ are integers.

Given that $M=$ $\frac{18^{4 n} \times 2^{3 ( n^{2} - 6 n )} \times 3^{2 ( 1 - 4 n )} }{12^{2}}$

find the values of $n$ for which $M=2$

The diagram shows a trapezium.

All measurements shown on the diagram are in centimetres. The area of the trapezium is $133\mathrm{cm}^{2}$

Show that $8x^{2}--6x--275=0$

Find the value of $x.$

Show your working clearly.

Express $7--4x--x^{2}$ in the form $p--(x+q)^{2}$ where $p$ and $q$ are constants.

Use your answer to part (a) to solve the equation $7--4(y+3)--(y+3)^{2}=0$

Give your solutions in the form $e\pm\sqrt{f}$ where $e$ and$f$ are integers.

Solve $\frac{5}{4x+1}=\frac{2x}{x^{2}+3}$

Give your solutions to 3 significant figures. You must show your working.

$y=6x^{4}+7x^{2}$ and $x=\sqrt{w+1}$

Find the value of $w$ when $y=10$. Show your working.

$w$ = ................

$6x^{2}=7xy+20y^{2}$ where $x>0$ and $y>0$

Find the ratio $x:y$