# Quadratic Equations

- An expression of the form ax² +bx +c where a
0 is called a
**quadratic**(or**second degree**)**expression**in variable x. An equation of the type ax² +bx +c = 0, a 0, is called a**quadratic equation**in variable x.

Thus x² -1 = 0; 1 -2x +3x² = 0 are quadratic equations. - A number is called a
**root**or**solution**of quadratic equation ax² +bx +c = 0 if it*satisfies*given equation, that is if a² +b +c = 0.

### Solving quadratic equations by factorisation

- This method involves using a property of numbers known as
**zero product rule:**

If ab = 0 then a = 0 or b = 0.

Hence we may factorise a quadratic expression and use above rule to solve the quadratic equation.

## Exercise

- Determine whether x = 1/2 and x = 3/2 are the solutions of the quadratic 2x² -5x +3 = 0 or not.

*Solve the following quadratic equations by factorisation:*

- 4x² = 3x
- x²-5 x = 0
- x (2x +1) = 6
- x² -3x -10 = 0
- 3x² -5x -12 = 0
- x² -2x +1 = 0
- 3x² = x +4
- 2 x² -x = 3
- 6 +x -x² = 0
- 4x² +4x +1 = 0
- (x -3)(2x +5) = 0
- (x +2)(x -3) = 6
- x +1/x = 41/20
- 3x -8/x = 2
- (x +2)/(x +3) = (2 x -3)/(3 x - 7)
- 8/(x +3) - 3/(2 -x) = 2

## Answers

**1.**x = 1/2 is not a solution; x = 3/2 is a solution.

**2.**0, 3/4

**3.**0, 5

**4.**-2, 3/2

**5.**-2, 5

**6.**3, -4/3

**7.**1, 1

**8.**-1, 4/3

**9.**-1, 3/2

**10.**-2, 3

**11.**-1/2, -1/2

**12.**3, -5/2

**13.**-3, 4

**14.**4/5, 5/4

**15.**2, - 4/3 .

**16.**-1, 5

**17.**-1/2, 5