The quadratic equation whose one root is −3+i74 is

α=−3+i74,β=−3−i74 α+β=−32 , αβ=1 Equation is x2+32x+1=0 ⇒ 2x2+3x+2=0

The quadratic equation whose one root is −3+i74 is

α=−3+i74,β=−3−i74 α+β=−32 , αβ=1 Equation is x2+32x+1=0 ⇒ 2x2+3x+2=0

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

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

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

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

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

answer is D.

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Detailed 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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The quadratic equation whose one root is −3+i74 is

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