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Use the quadratic formula to solve for the roots in the following equation.

4x2+5x + 2 = 2x2+7x-1

User Shonna
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1 Answer

5 votes

Answer:

The roots of
4 x^(2)+5 x+2=2 x^(2)+7 x-1 are
(2+2 i √(5))/(2) and
(2-2 i √(5))/(2)

Solution:

The equation given is,


4 x^(2)+5 x+2=2 x^(2)+7 x-1

Simplifying we get,


4 x^(2)+5 x+2=2 x^(2)+7 x-1


4x^2- 2x^2 +5x- 7x +2+1 = 0


(4x^2-2x^2) +(5x -7x) +(2+1) = 0


2x^2 -2x +3 =0

We know that the quadratic formula to solve this,

X has two values which are
=\frac{(-b+\sqrt{b^(2)-4 a c})}{2 a} \text { and } \frac{-b-\sqrt{b^(2)-4 a c}}{2 a}

Here a= 2; b = -2; c = 3

So substituting the values we get,


x=\frac{-(-2)+\sqrt{(-2)^(2)-4 * 2 * 3}}{2 * 2}


\Rightarrow(2+√(4-24))/(4)=(2+√(-20))/(4)=(2+√((-1) * 4 * 5))/(4)


\Rightarrow=(2+2 i √(5))/(2)
(\text { assuming }-√(-1)=\mathrm{i})

Again
x=(2-2 i √(5))/(2)

So, the roots are
(2+2 i √(5))/(2) and
(2-2 i √(5))/(2)

User Kittu Rajan
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