Quadratic Equations in One Variable
Quadratic equation is in the form
a, b, & c = real-number constants
a & b = numerical coefficient or simply coefficients
a = coefficient of x2
b = coefficient of x
c = constant term or simply constant
a cannot be equal to zero while either b or c can be zero
Examples of Quadratic Equation
Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.
For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.
Roots of a Quadratic Equation
The equation ax2 + bx + c = 0 can be factored into the form
Where x1 and x2 are the roots of ax2 + bx + c = 0.
For the quadratic equation ax2 + bx + c = 0,
See the derivation of quadratic formula here.
The quantity b2 - 4ac inside the radical is called discriminat.
• If b2 - 4ac = 0, the roots are real and equal.
• If b2 - 4ac > 0, the roots are real and unequal.
• If b2 - 4ac
Sum and Product of Roots
If the roots of the quadratic equation ax2 + bx + c = 0 are x1 and x2, then
Sum of roots
Product of roots
You may see the derivation of formulas for sum and product of roots here.