2. An equation of the form ax2 + bx + c = 0, where a, b, c are real
numbers and a≠ 0 is called quadratic equation.
If b = 0, then we have an equation of the form ax2 + c = 0.
To solve quadratic equation is to find the roots, zeros, or solution of the
quadratic equation. The roots, zeros, or solution of a quadtatic equation
are the values of x that will make the equation ax2 + c = 0 true.
To solve a quadratic equation of the form ax2 + c = 0, we use the
square root property.
Square Root Property
If x2 = k, then x = ± 𝑘, where k is a non-negative integer.
3. Example 1. Solve the quadratic equation x2 – 25 = 0
Steps Solution
1. Write the equation in the form of
ax2 = c
x2 – 25 = 0
x2 – 25 + 25 = 0 + 25
x2 = 25
2. Apply the square root property x2 – 25 = 0
x2 = 25
X = ± 25 ; x = 5 and x = -5
So, the roots are 5 and -5
4. Example 2. Solve the quadratic equation x2 – 16 = 0.
Steps Solution
1. Write the equation in the form of
ax2 = c
x2 – 16 = 0
x2 – 16 + 16 = 0 + 16
x2 = 16
2. Apply the square root property
x2 = 16
x = ± 16 ; x = 4, and x= -4
So, the roots are 4 and -4.
5.
6. Example 3. Solve the quadratic equation 3x2 = 27.
Steps Solution
1. Write the equation in the form of
ax2 = c
3x2 = 27
3 3
Multiply the quadratic equation by the
reciprocal of a.
1
3
(3x2) =
1
3
(27)
x2 = 9
2. Apply the square root property x2 = 9
= ± 9
x = ±3 ; roots = 3 and -3
