Complex Numbers and Quadratic Equations

27. Kindly go through the solution

26. Kindly go through the solution

25. Kindly go through the solution

24. Kindly go through the solution

23. x² – x + 2 = 0

Comparing the given equation with ax² + bx + c = 0

We have, a = 1, b = –1 andc = 2

Hence, discriminant of the equation is

b² – 4ac = (-1)² – 4 * 1 * 2 = 1 – 8 = –7

Therefore, the solution of the quadratic equation is

21. –x² + x – 2 = 0

Comparing the given equation with ax² + bx + c = 0

We have, a = –1, b = 1 and c = –2

Hence, discriminant of the equation is

b² – 4ac = 1² – 4 * (-1)* (-2) = 1 – 8 = –7

Therefore, the solution of the quadratic equation is

20. x² + 3x + 9 = 0

Comparing the given equation with ax² + bx + c = 0

We have, a = 1, b = 3 and c = 9

Hence, discriminant of the equation is

b² – 4ac = 3² – 4 * 1* 9 = 9 – 36 = –27

Therefore, the solution of the quadratic equation is

18. x² + 3 = 0

=>x² = –3

=>x = $\pm \surd 3$

=>x= ± √3$i$ [since, √-1 = i]

=>x = 0 ± √3$i$

17. Kindly go through the solution

16. Kindly go through the solution