Quadratic Equations - Questions - Class Mathematics School Portal

Quadratic Equations - Questions

Question 1

15566

Solve \(8{t^2} - 26\; = \;38,\) leaving your answer in surd form

Answer

\(t = \pm \sqrt 8 \)

Worked Solution

Question 2

15567

Solve \(4 + \dfrac{{{d^2}}}{3}\; = \;8,\,\) correct to \({\rm{1}}\) dp

Answer

\(d = \pm 3.5\)

Worked Solution

Question 3

15568

Solve \(2{n^2} + 3\; = \;7{n^2} - 18,\) correct to \({\rm{2}}\) dp

Answer

\(n = \pm 2.05\)

Worked Solution

Question 4

15569

Solve \(\dfrac{{{y^2}}}{5} - 9\; = \;2,\,\) correct to \({\rm{1}}\) dp

Answer

\(y = \pm 7.4\)

Worked Solution

Question 5

15570

Solve \(\dfrac{{5{a^2}}}{2} + 3 = 2,\) correct to \({\rm{1}}\) dp

Answer

\(\text{No solution}\)

Worked Solution

Question 6

59437

Solve \(2{p^2}\; = \;50\)

Answer

\(p = \pm 5\)

Worked Solution

Question 7

59436

Solve \(7{t^2}\; = \;343\)

Answer

\(t = \pm 7\)

Worked Solution

Question 8

59435

Solve \({y^2} = 59\) (1dp)

Answer

\(y = \pm 7.7\)

Worked Solution

Question 9

59434

Solve \(3{k^2} = \;75\)

Answer

\(k = \pm 5\)

Worked Solution

Question 10

59438

Solve \(8{t^2} - 26\; = \;38\), leaving your answer in surd form.

Answer

\(t = \pm \sqrt 8 \)

Worked Solution

Question 11

49294

Solve \(x^2=81\)

Answer

\(\pm 9\)

Worked Solution

\(\begin{aligned}
x^2&=81\\
x&=\sqrt{81}\\
x&=\pm 9
\end{aligned}\)

Question 12

49296

Solve \(2x^{2}-1 =71\)

Answer

\(\pm 6\)

Worked Solution

\(\begin{aligned}
2x^{2}-1 &=71 \\
2x^{2}-1+1 &=71+1 \\
2x^{2} &=72 \\
\frac{2x^{2}}{2} &=\frac{72}{2} \\
x^{2} &=36 \\
x &=\pm \sqrt{36} \\
x &=\pm 6
\end{aligned}\)

Question 13

49295

Solve \(\dfrac{x^2}{2}=8\)

Answer

\(\pm 4\)

Worked Solution

\(\begin{aligned}
\frac{x^2}{2}&=8\\
2 \times \frac{x^2}{2}&=2\times 8\\
x^2&=16\\
x&=\sqrt{16}\\
x&=\pm 4
\end{aligned}\)

Question 14

49299

Solve \(\dfrac{x^{2}-1}{3} =7\), giving your solutions correct to 1 decimal place

Answer

\(\pm 4.7\)

Worked Solution

\(\begin{aligned}
\frac{x^{2}-1}{3} &=7 \\
3 \times \frac{x^{2}-1}{3} &=3 \times 7 \\
x^{2}-1 &=21 \\
x^{2}-1+1 &=21+1 \\
x^{2} &=22 \\
x &=\pm \sqrt{22} \\
x &=\pm 4.7
\end{aligned}\)

Question 15

49298

Solve \(\dfrac{x^{2}}{3}+1 =7\), giving your solutions correct to 1 decimal place

Answer

\(\pm 4.2\)

Worked Solution

\(\begin{aligned}
\frac{x^{2}}{3}+1 &=7 \\
\frac{x^{2}}{3}+1-1 &=7-1 \\
\frac{x^{2}}{3} &=6 \\
3 \times \frac{x^{2}}{3} &=6 \times 3 \\
x^{2} &=18 \\
x &=\pm \sqrt{18} \\
x &=\pm 4.2
\end{aligned}\)

Question 16

49297

Solve \(2x^{2}+1=7\), giving your solutions correct to 1 decimal place.

Answer

\(\pm 1.7\)

Worked Solution

\(\begin{aligned}
2x^{2}+1 &=7 \\
2x^{2}+1-1 &=7-1 \\
2x^{2} &=6 \\
\frac{2x^{2}}{2} &=\frac{6}{2} \\
x^{2} &=3 \\
x &=\pm \sqrt{3} \\
&=\pm 1.7
\end{aligned}\)