A quadratic equation is an equation of degree 2, meaning that the highest exponent of this function is 2.
The standard form of a quadratic is y = ax2 + bx + c,
where a, b, and c are numbered and a cannot be 0.
Examples of quadratic equations include all of these:
- y = x2 + 3x + 1
- y = x2
Sum and Product of roots:
If α and β are the roots of a quadratic equation, then
- S = α+β= -b/a = coefficient of x/coefficient of x2
- P = αβ = c/a = constant term/coefficient of x2
The given equation is ax² + bx + c = 0
It is given that α and β are the roots of the equation ax2 + bx + c = 0.
aɑ2 + bɑ + c = 0
aɑ + b = – c / ɑ
ɑβ2 + bβ + c = 0
(ɑβ + b) = – c / β
α / [ɑβ + b] + β / [aɑ + b] = (ɑβ / – c) + (ɑβ / – c) = – 2ɑβ / c
= – 2 / a
Check out the video given below to know more about quadratic equations