Question 1

LEVEL 6

Use the quadratic formula to solve the following quadratic.

5x^{2}-11x-31=0

Select the correct answer to 3dp from the list below:

A: x= -1.62, x= 3.82

B: x= -1.622, x=3.822

C: x= -1.622, x=-3.822

D: x= 1.622, x=3.822

 

CORRECT ANSWER:   B: x= -1.622, x=3.822

WORKED SOLUTION:

The quadratic formula is

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

 

Substitute the values of a,b and c into it to get

x=\dfrac{11+\sqrt{11^2-4\times5\times-31}}{2\times5}

 

x=3.822

 

Do the same again but using the minus sign this time

x=\dfrac{11-\sqrt{11^2-4\times5\times-31}}{2\times5}

 

x= -1.622

Answer: B

Question 2

LEVEL 6

Use the quadratic formula to solve the following quadratic.

0=x^{2}+4x+2

Select the correct answer to 2dp from the list below:

A: x= 3.41, x=0.58

B: x= -3.414, x=0.585

C: x= -3.41, x=0.59

D: x= 3.41, x=0.58

 

CORRECT ANSWER:  C: x= -3.41, x=0.59

WORKED SOLUTION:

The quadratic formula is

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

Substitute the values of a,b and c into it to get

x=\dfrac{-4+\sqrt{4^2-4\times1\times2}}{2\times1}

 

x=0.59

 

Do the same again but using the minus sign this time

x=\dfrac{-4-\sqrt{4^2-4\times1\times2}}{2\times1}

 

x= -3.41

Answer: B

Question 3

LEVEL 6

Use the quadratic formula to solve the following quadratic, without using a calculator.

0=x^{2}+4 x+3

Select the correct answer below:

A: x=1 and x=3

B: x=-1 and x=3

C: x=-1 and x=-3

D: x=1 and x=-3

 

CORRECT ANSWER: C: x=-1 and x=-3

WORKED SOLUTION:

The quadratic formula is

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

Substitute the values of a,b and c into it to get

x=\dfrac{-4+\sqrt{4^2-4\times1\times3}}{2\times1}

 

The calculate each part of the equation starting with the square root first to give

x=\dfrac{-4+\sqrt{4}}{2\times1}

 

Simplify this further to calculate

x=-1

 

Do the same again but using the minus sign this time

x=\dfrac{-4-\sqrt{4^2-4\times1\times3}}{2\times1}

 

x= -3

Answer: C

Question 4

LEVEL 6

Use the quadratic formula to solve the following quadratic.

0=2x^{2}+6x-1

Select the correct answer to 2 dp from the list below:

A: x=-3.15, x=0.15

B: x=-0.18, x=-2.82

C: x=-3.16, x=0.16

D: x=-3.16, x=-0.16

 

CORRECT ANSWER: C: x=-3.16, x=0.16

WORKED SOLUTION:

The quadratic formula is

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

Substitute the values of a,b and c into it to get

x=\dfrac{-6+\sqrt{6^2-4\times2\times-1}}{2\times2}

 

x=0.16

 

Do the same again but using the minus sign this time

x=\dfrac{-6-\sqrt{6^2-4\times2\times-1}}{2\times2}

 

x= -3.16

Answer: C

Question 5

LEVEL 6

Use the quadratic formula to solve the following quadratic.

0=8x^{2}-15x-8

Select the correct answer to 1 dp from the list below:

A: x=-0.4, x= 2.3

B: x=1.4, x= -0.7

C: x=0.4, x= -2.3

D: x=-0.4, x= -2.3

 

CORRECT ANSWER:  A: x=-0.4, x= 2.3

 

WORKED SOLUTION:

The quadratic formula is

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

 

Substitute the values of a,b and c into it to get

x=\dfrac{15+\sqrt{6^2-4\times8\times-8}}{2\times8}

 

x=2.3

 

Do the same again but using the minus sign this time

x=\dfrac{15-\sqrt{6^2-4\times8\times-8}}{2\times8}

 

x= -0.4

 

Answer: A