First slide

Theory of equations

Question

The quadratic equation whose one root is $\frac{- 3 + i \sqrt{7}}{4}$ is

Easy

A

$2 x^{2} - 3 x + 2 = 0$
B

$2 x^{2} + 3 x - 2 = 0$
C

$2 x^{2} - 3 x - 2 = 0$
D

$2 x^{2} + 3 x + 2 = 0$

Solution

$α = \frac{- 3 + i \sqrt{7}}{4}, β = \frac{- 3 - i \sqrt{7}}{4}$
$α + β = \frac{- 3}{2}, α β =1$

Equation is $x^{2} + \frac{3}{2} x + 1 = 0$

$\Rightarrow$ $2 x^{2} + 3 x + 2 = 0$

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