How to Solve Quadratic Equations – Tutorial, Examples and Practice Questions
Method 1 – Factoring
Quadratic equations are usually called second degree equations, which mean that the second degree is the highest degree of the variable that can be found in the quadratic equation. The form of these equations is:
where a, b and c are some real numbers.
One way for solving quadratic equations is the factoring method, where we transform the quadratic equation into a product of 2 or more polynomials. Let’s see how that works in one simple example:
Notice that here we don’t have parameter c, but this is still a quadratic equation, because we have the second degree of variable x. Our factor here is x, which we put in front and we are left with x+2. The equation is equal to 0, so either x or x+2 are 0, or both are 0.
So, our 2 solutions are 0 and -2.
Method 2 – Quadratic formula
If we are unsure how to rewrite quadratic equations so we can solve it using factoring method, we can use the formula for quadratic equation:
We write x1,2 because it represents 2 solutions of the equation. Here is a practice question :
We see that a is 3, b is -10 and c is 3.
We use these numbers in the equation and do some calculations.
Notice that we have + and -, so x1 is for + and x2 is for -, and that’s how we get 2 solutions.
Answer Key
Answer Key
1. B
The numbers are 15 and 6.
x + 7 = 21 => x = 21 -7
x2 + y2 = 261
(21 – 7 )2 + y2 = 261
441 – 42y + y2 + y2 = 261
2y2 – 42y + 180 = 0
y2 – 21y + 90 = 0
y1,2 = 21 + ?441 – 360/2
y1,2 = 21 + ?81/2
y1,2 = 21 + 9/2
y1 = 15
y2 = 6
x1 = 21 = y1 = 21 – 15 = 6
x2 = 21 – y2 = 21 – 6 = 15
2. D
-2
3. B
4. A
0 and 1.5
2x2 – 3x = 0
x(2x – 3)
x = 0 or 2x – 3 =0
x = 0 or x = 3/2
x = 0 or x = 1.5
5. A
2 and 7
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1 Comment
Very helpful