Quadratic equation?

Question

What is the relation between the coefficients and the roots of a quadratic equation

Answer 1

For ax² +bx + c = 0

a , b, c are coefficients

-b ± √ (b² - 4ac)
------------------------------ = x
2a

Here teh roots will be x1 & x2

-b + √ (b² - 4ac)
------------------------------ = x1
2a

-b - √ (b² - 4ac)
------------------------------ = x2
2a

Answer 2

x = ( -b ± sqrt ( b² - 4ac) ) / 2a: the quadratic formula to solve an equation of the form ax² + bx + c = 0 and giving usually two distinct solutions.

Answer 3

For equation ax^2 + bx + c = 0
if its discriminant D = b^2 -- 4ac is
(i) D < 0, roots are imaginary , unequal
(ii) D = 0, roots are real, rational and equal.
(iii) D > 0 but not a perfect square, roots are real, irrational and unequal.
(iv) D > 0 and a perfect square, roots are real, rational, unequal.

Answer 4

Consider equation:-
ax² + bx + c = 0
x² + (b/a)x + c/a = 0
Consider equation with roots α and β
(x - α ) (x - β) = 0
x² - β x - α x + α β = 0
x² - (α + β) x + α β = 0

(α + β) = - b /a
α β = c / a