Quadratic Equation Exercises
Quadratic equation is also called as second degree equation.
The basic form of a second degree equation is given by ay2 + b y + c = 0. Where, a = coefficient of y2, b = coefficient of y, c = constant and y is the variable.
Let us consider the equation 6y2 + 12y 9=0. In this equation, maximum power of the variable y is 2. So, it is a second degree equation.
Three methods are used to solve the quadratic equation.
1) Factoring method
2) Quadratic formula method
3) Completing the square method
Exercise Problems to Solve Quadratic Equation:
Exercise problem 1:
Determine the given equation is a quadratic equation or not.
(x - 10) (x - 20) = 0
Solution:
Multiply two expressions in the left hand side,
(x - 10) (x - 20) = 0
x(x-20) -10(x-20)=0
x2 -20x -10x + 10(20) = 0
x2 -30x +200 = 0
So, the highest exponent of variable x is 2.
So, the given equation is a quadratic equation.
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Exercise problem 2:
Solve the quadratic equation by factoring: x2 + 28x + 27 = 0
Solution:
x2 + 28x + 27 = 0
Here a = coefficient of x2 = 1
b = coefficient of x = 28
c = constant term = 27
We find a c = 1 27 = 27, a + c = 1 + 27 = 28 = b.
By splitting the middle term, we get
x2 + 28x + 27 = 0
x2 + 1x + 27x + 27 = 0
x(x + 1) + 27(x + 1) = 0
(x + 1) (x + 27) = 0
x = 1, x = 27
The solution set = {1, 27}.
Few more Exercise Problems to Solve Quadratic Equations:
Exercise problem 3:
Solve the quadratic equation using quadratic formula: x2 - 28x + 27 = 0
Solution:
Coefficients are: a = 1, b = -28, c = 27
Quadratic Formula: x = [-b (b2-4ac)] / 2a
Put in a, b and c: x = [-(-28) [(-28)2-41 (27)] / (21)
Solve: x = [28 (784-108)]/2
x = [28 (676)]/2
x = (28 26)/2
x= (28+ 26)/2
x = (28-26)/2
x= (54)/2
x= (2)/2
x= 27
x= 1
So, the answer is x = 27, 1.
Exercise problem 4:
Solve the equation by completing the square x2 - 32x + 31 = 0.
Solution: x2 - 32x = -31. The term to be added =(-32/2)2= 256
Adding 256 on both sides we get
x2 - 32x + 256 = -31 + 256
(x 16)2 = 225
Taking square root on both sides x 16 = 15
x - 16 = 15 x 16 = 15
x=31
x=1
So, the answer is x=1 (or) 31.
by: mathqa
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