Solve the equation x^{2}-2x+frac{3}{2}=0. | vedclass

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Question

(A) The given quadratic equation is $x^{2}-2x+\frac{3}{2}=0$. Multiplying by $2$,we get $2x^{2}-4x+3=0$. Comparing this with $ax^{2}+bx+c=0$,we have $

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$1 \pm \frac{\sqrt{2}}{2}i$

Vedclass · Answer

(A) The given quadratic equation is $x^{2}-2x+\frac{3}{2}=0$. Multiplying by $2$,we get $2x^{2}-4x+3=0$. Comparing this with $ax^{2}+bx+c=0$,we have $a=2, b=-4, c=3$. The discriminant $D = b^{2}-4ac = (-4)^{2}-4(2)(3) = 16-24 = -8$. The roots are given by $x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-(-4) \pm \sqrt{-8}}{2(2)}$. $x = \frac{4 \pm 2\sqrt{2}i}{4} = \frac{4}{4} \pm \frac{2\sqrt{2}i}{4} = 1 \pm \frac{\sqrt{2}}{2}i$.

Solve the equation $x^{2}-2x+\frac{3}{2}=0$.

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