Question

Solve the following equation and give your answer correct to 3 significant figures
$5{{x}^{2}}-3x-4=0$

Answer 1

Hint: First write the equation and compare it to the general quadratic equation by comparing the values of a, b, c and substitute them into a quadratic formula. Simplify this formula to get the value of ‘x’. This value of x is the required solution.

Complete step-by-step answer:
Given equation in the question is written as follows
$5{{x}^{2}}-3x-4=0$
The general quadratic equation in terms of a, b, c is written as,
$a{{x}^{2}}+bx+c=0$
The roots of the above equation can be written in terms of a, b, c as
$x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
By comparing equations, we can say values of a, b, c as
a = 5, b = -3, c = -4
By substituting in the value of x, we can write it as
$x=\dfrac{3\pm \sqrt{{{\left( 3 \right)}^{2}}-4\left( 5 \right)\left( -4 \right)}}{10}$
By taking square root separately, we get in form of
$=\sqrt{{{\left( 3 \right)}^{2}}-4\left( 5 \right)\left( -4 \right)}$
By taking the square of the number, we get it as
$=\sqrt{9-4\left( 5 \right)\left( -4 \right)}$
By simplifying the product term, we get it in the form
$=\sqrt{9+80}$
By simplifying we can write the above term in the form
$=\sqrt{89}$
By taking square root value up to 3 significant as asked
9.433
By substituting this into x, we get it in the form of
$x=\dfrac{3\pm 9.433}{10}=\dfrac{3+9.433}{10},\dfrac{3-9.433}{10}$
By simplifying the above one, we get the value of x as
x = 1.243, -0.643. Therefore these are the roots of the equation.

Note: While applying quadratic formula take care of sign –b in the starting. Generally students confuse this step. It is better to solve the square root separately for more clarity. While taking values of x separately take care while taking the “-“ in $\pm $ symbol. Because students make a lot of mistakes in “-“ they forget to subtract the root itself. So be careful.