Quadratic Formula Questions, Worksheets and Revision

Firstly, the quadratic formula is

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Then, we can identify that here, a=1, b=11, and c=16. Putting these values into the formula, we get

x=\dfrac{-11\pm\sqrt{11^2-4\times1\times16}}{2}

The part inside the square root is

11^2-4\times1\times16=121-64=57

So, the solutions become

x=\dfrac{-11\pm\sqrt{57}}{2}

Putting these into a calculator (one with +, one with -), we get the final solutions

x=-1.7250...=1.73\text{ (3sf), and }\,x=-9.2749...=-9.27\text{ (3sf)}

Firstly, the quadratic formula is

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Then, we can identify that here, a=1, b=-2, and c=-44. Putting these values into the formula, we get

x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4\times1\times(-44)}}{2}

The part inside the square root is

(-2)^2-4\times1\times(-44)=4+176=180

So, the solutions become

x=\dfrac{2\pm\sqrt{180}}{2}

Putting these into a calculator (one with +, one with -), we get the final solutions

x=7.7082...=7.71\text{ (3sf), and }\,x=-5.7082...=-5.71\text{ (3sf)}

Firstly, the quadratic formula is

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Then, we can identify that here, a=4, b=7, and c=-1. Putting these values into the formula, we get

x=\dfrac{-7\pm\sqrt{7^2-4\times4\times(-1)}}{2\times4}

The part inside the square root is

7^2-4\times4\times(-1)=49+16=65

So, the solutions become

x=\dfrac{-7\pm\sqrt{65}}{8}

Putting these into a calculator (one with +, one with -), we get the final solutions

x=0.1327...=0.13\text{ (2dp), and }\,x=-1.8827...=-1.88\text{ (2dp)}

Firstly, the quadratic formula is

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Then, we can identify that here, a=1, b=8, and c=13. Putting these values into the formula, we get

x=\dfrac{-8\pm\sqrt{8^2-4\times1\times13}}{2\times1}

The part inside the square root is

8^2-4\times8\times13=64-52=12

So, the solutions become

x=\dfrac{-8\pm\sqrt{12}}{2}

Putting these into a calculator (one with +, one with -), we get the final solutions

x=-2.2679...=-2.27\text{ (2dp), and }\,x=-5.73205...=-5.73\text{ (2dp)}

Firstly, the quadratic formula is

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Then, we can identify that here, a=25, b=-30, and c=7. Putting these values into the formula, we get

x=\dfrac{-(-30)\pm\sqrt{(-30)^2-4\times25\times7}}{2\times25}

The part inside the square root is

30^2-4\times25\times7=900-700=200

So, the solutions become

x=\dfrac{30\pm\sqrt{200}}{50}

Putting these into a calculator (one with +, one with -), we get the final solutions,

x=\dfrac{3\pm\sqrt{2}}{5}