Question

One of the roots of a quadratic equation that has integral coefficients is $\frac{-4}{5}+\frac{3\sqrt{2}}{8}i$. Which of the following describes the quadratic equation?

• A. $800x^2+1280x+737=0$
• B. $800x^2-1280x+737=0$
• C. $800x^2+1280x+287=0$
• D. $800x^2-1280x+287=0$
• E. $800x^2+1280x-287=0$

Answer 1

The correct option is A $800x^2+1280x+737=0$

$a{x}^2+bx+c=0a,b,c$ are real

one root is $\frac{-4}{5}+\iota \frac{3\sqrt{2}}{8}$ then another root will be $\frac{-4}{5}-\iota \frac{3\sqrt{2}}{8}$

Sum of roots $=\frac{-8}{5}$

Product of roots $={\left(\frac{4}{5}\right)}^2+\frac{18}{64}$

$=\frac{16}{25}+\frac{9}{32}=\frac{512+225}{800}$

$=\frac{757}{800}$

$\Rightarrow 800x^2+1280x+737=0$