Question

Solve the quadratic equation $ 3{{x}^{2}}-x-7=0 $ and give your answer correct to three significant figures.

Answer 1

Hint: Here, in this question, we must first solve the quadratic equation and find the values of x. We will make use of the quadratic formula for solving the same. Then we may get some irrational number in the roots of the equation. If we get, then we have to calculate its square root up to 4 significant figures and then round off to 3 significant figures which will be our answer to the question.

Complete step-by-step answer:
In this given question, we are asked to solve the quadratic equation $ 3{{x}^{2}}-x-7=0 $ and give our answer correct to three significant figures.
Now, for a quadratic equation $ a{{x}^{2}}+bx+c=0 $ , the general quadratic formula is $ x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}.....(1.1) $ .
Now, using equation 1.1 for $ 3{{x}^{2}}-x-7=0 $ we get,
 $ x=\dfrac{-(-1)\pm \sqrt{{{(-1)}^{2}}-4\times 3\times (-7)}}{2\times 3}.........(1.2) $
Now, simplifying equation 1.2, we get,
 $ \begin{align}
  & x=\dfrac{-(-1)\pm \sqrt{{{(-1)}^{2}}-4\times 3\times (-7)}}{2\times 3} \\
 & \Rightarrow x=\dfrac{1\pm \sqrt{1+84}}{6} \\
 & \Rightarrow x=\dfrac{1\pm \sqrt{85}}{6}........(1.3) \\
\end{align} $
From 1.3, by putting $ \sqrt{85}=9.204=9.20 $ , we get x is equal to 1.70 and 1.36.
Therefore, the value of x correct to three significant figures is 1.70 or 1.36.

Note: In this sort of question, we must be careful while making the answer correct up to the given number of significant figures. Here, the 0 at the end of 9.20 or 1.70 are significant as the zeros after decimal point are significant.