Quadratic Equations Practice Questions

Solve $x^2 - x - 20 = 0$

Solve $x^2 = 8x$

Solve $(x+2)^2 = 36$

Kara is looking at the equation $(x+2)^2 = -5$

She says, "This equation also has two solutions."

Is Kara correct? Give a reason for your answer.

Solve $6x^2 + 11x - 10 = 0$

Show that the equation $x^2 - 6x + 11 = 0$ has no solutions.

Solve $(2x+1)(x-4) = 3x - 8$

Give your solutions correct to 2 decimal places.

You must show all your working.

Solve $x^2 + 8x - 3 = 0$ by completing the square.

Give your solutions in the form $a \pm \sqrt{b}$, where $a$ and $b$ are integers.

Use the graph to write down estimates for the solutions of $x^2 - 3x - 1 = 0$

By drawing a suitable straight line on the graph, find estimates for the solutions of $x^2 - 3x - 4 = 0$

The length of a rectangle is $(x+4)$ cm and the width of the rectangle is $(2x-3)$ cm.

The area of the rectangle is $51$ cm².

Work out the perimeter of the rectangle.

You must show all your working.

Work out the area of the triangle.

You must show all your working.

A bag contains only red counters and blue counters.

There are $3$ red counters in the bag.

There are $n$ blue counters in the bag.

There are more than $4$ counters in the bag.

Sofia is going to take at random two counters from the bag.

The probability that she takes one counter of each colour is $\dfrac{1}{2}$

Work out the value of $n$.

Solve $\dfrac{3}{x+2} + \dfrac{4}{x-1} = 2$

Give your solutions correct to 3 significant figures.

You must show all your working.