Question

Find the quadratic equation whose one root is $\frac{1-i\sqrt{29}}{2}$.

• A. 2x² - 2x + 10 = 0
• B. 2x² - 15x + 2 = 0
• C. 2x² - 2x + 15 = 0
• D. = 0

Answer 1

The correct option is C

2x² - 2x + 15 = 0

Since, Complex root occurs in conjugate other roots should be conjugate of given root.

$\alpha$ = $\frac{1-i\sqrt{29}}{2}$, $\beta$ = $\frac{1+i\sqrt{29}}{2}$

$\alpha$ + $\beta$ = 1 $\alpha$.$\beta$ = $\frac{15}{2}$

Quadratic Equation

$x^2-(\alpha +\beta )x+\alpha \beta$ = 0

$x^2-x+\frac{15}{2}$ = 0

$2x^2-2x+15=0$