## Practice problem5

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In this page practice problem5 we are going to solve and practice quadratic equations with complex roots.

. While solving a quadratic equation we will get either real or imaginary roots. So
before start solving the equations, let us find the value of the
discriminant which tells us about the nature of the roots.

**Solutions:**

1. x²/2=2x-4

Here the left hand side of the equation is in fraction form. To remove the denominator we have to multiply the whole equation by 2.

2(x²/2) = 2(2x-4)

x² = 4x -8

Now let us write all terms of the equation in one side.

x²-4x+8 =0

** Here a= 1, b= -4 and c=8**

The value of the discriminant is √(-16), which is negative. So we will get complex roots. Now let us solve for x.

= (4±4i)/2

= 2±2i

The roots are = **2+2i, 2-2i**

Now let us solve the next equation.

x²-x+3=0

**Here a= 1, b= -1 and c=3**

Here the value of the discriminant is √(-11), which is negative. So we will get complex roots. Now let us solve for x.

The roots are = **(1+i√11)/2, (1-i√11)/2 **

Now let us do the next problem.

2x²-2x+5=0

**Here a= 2, b= -2 and c=5**

Here the value of the discriminant is √(-36), which is negative. So we will get complex roots. Now let us solve for x.

The roots are = **(1+3i)/2, (1-3i)/2**

Problems for practice:

- x²-3x+1=0
- 2x²-x+4=0

Teachers and
parents can guide the student to practice the problems given in practice problem5 and get a good
knowledge about the complex numbers. Two problems are given for practice. students can solve them using the method discussed above. If you have any doubt in any
problem, you can contact us, we will clear all your doubts.