Quadratic Equations
By DarthVader
Date: 2022-07-03
Topic: 141 see comments
Post views: 1034
Quadratic Equations
A quadratic equation is one that can be expressed in the form:
ax2 + bx + c = 0
More generally, a quadratic function is any equation that has the form:
y = ax2 + bx + c
(The coefficient ‘a’ can be positive or negative but not equal to zero)
(The coeffiecients ‘b’ and ‘c’ can be positive negative or zero)
The word quadratic comes from the latin word for ‘squared’ and a quadratic equation is one which contains a squared term.
Completing The Square
How to complete the square for a quadratic:
- Write down (x x x)2 , filling in the gap with the number that is half of b, the coefficient of x.
- Subtract the square of the number that you wrote in the gap.
Example:
For the quadratic: x2 + 8x
The completed square is: (x + 4) - 16
The Discriminant
The discriminant of a quadratic equation is b2−4ac which is the part which lies under the square root sign in the quadratic formula.
Number Of Real Solutions Of A Quadratic Equation
The quadratic equation ax2 + bx + c = 0 has:
- Two real solutions if b2 − 4ac > 0 (the discriminant is positive)
- One real solution if b2 − 4ac = 0 (the discriminant is zero)
- No real solutions of b2 − 4ac < 0 (the discriminant is negative)
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