Answer:
x= -b ±√b²- 4ac/2a
Step-by-step explanation:
ax2 + bx + c = 0
Dividing the quadratic equation by a gives
x2 + b/ax + c/a = 0
x2 + b/ax = - c/a
Applying the square formula
(x)^2 + 2(x) (b/2a) + (b/2a)^2= + (b/2a)^2- c/a
(x+b/2a)^2= b²/4a² - c/a
(x+b/2a)^2= b²/4a² - 4ac/4a²
(x+b/2a)^2= b²- 4ac/4a²
Taking square root of both sides gives
(x+b/2a)= ±√b²- 4ac/2a
x= -b/2a±√b²- 4ac/2a
x= -b ±√b²- 4ac/2a
This is called the quadratic formula and it can solve the value for x for the given value of a, b and c for the quadratic equation.
From this it is concluded that
Discriminant = b2 - 4ac > 0 means there will be two distinct real roots. Discriminant = b2 - 4ac = 0 means there will be only one real root. Discriminant = b2 - 4ac < 0 means there will be no real roots.
This is because a square root of a value greater than 0 is possible and gives two values for roots of x.
The square root of a value less than 0 gives a negative number and therefore the roots are an imaginary number.
The square root of a value greater equal to 0 gives a zero leaving behind only one real root.
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