Question

Find the roots of the following quadratic equation by using the quadratic formula
$4x^2+3x+5=0$

• A. $\frac{3\pm \sqrt{71}i}{8}$
• B. $\frac{3\pm \sqrt{89}i}{8}$
• C. $\frac{-3\pm \sqrt{71}i}{8}$
• D. $\frac{-3\pm \sqrt{89}i}{8}$

Answer 1

Answer: (C)

$\frac{-3\pm \sqrt{71}i}{8}$

Comparing $4x^2+3x+5=0$ with $a{x}^2+bx+c=0$ we get

$a=4,b=3,c=5$
Now the roots are $=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-3\pm \sqrt{(-3{)}^2-4\times 4\times 5}}{2\times 4}$

$=\frac{-3\pm \sqrt{9-80}}{8}$

$=\frac{-3\pm \sqrt{71}}{8}$

Thus, the quadratic equation does not have real roots.