Question

Solve each of the following equations for x and give, in each case, your answer correct to 2 decimal places:

(iii) $4x^2-5x-3=0$

Answer 1

Compare $4x^2-5x-3=0$ with $a{x}^2+bx+c=0$

$a=4,b=-5andc=-3$

We know that, for $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ are roots of the equation.

$\Rightarrow x=\frac{-(-5)\pm \sqrt{(-5{)}^2-4(4\left)\right(-3)}}{2\left(4\right)}$

$\Rightarrow x=\frac{5\pm \sqrt{25+48}}{8}$

$\Rightarrow x=\frac{5\pm \sqrt{73}}{8}$

$\Rightarrow x=\frac{5\pm 8.54}{8}$

$\Rightarrow x=\frac{13.54}{8}andx=\frac{-3.54}{8}$

$\therefore x=1.69and-0.44$.