Quadratic Equations - Questions

Question 1
59434

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

\(k = \pm 5\)

Question 2
59435

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

\(y = \pm 7.7\)

Question 3
59436

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

\(t = \pm 7\)

Question 4
59437

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

\(p = \pm 5\)

Question 5
59438

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

\(t = \pm \sqrt 8 \)

Question 6
49294

Solve \(x^2=81\)

\(\pm 9\)  

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

Question 7
49295

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

\(\pm 4\)

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

Question 8
49296

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

\(\pm 6\)

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

Question 9
49297

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

 \(\pm 1.7\)

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

Question 10
49298

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

\(\pm 4.2\) 

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

Question 11
49299

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

\(\pm 4.7\)  

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