Roots of a Quadratic Equation

You can also use completing the square

My explanation is shown below:

X^2 - 3x - 4 = 0

(x-4)(x+1)= 0

x=4 or x=-1

The quadratic formula is used to find the roots of a quadratic equation, which is generally written as Ax^2 + Bx + C = 0. The formula is given by:

x = (-B ± sqrt(B^2 - 4AC)) / (2A)

For the quadratic equation x^2 - 3x - 4 = 0, the coefficients are A = 1, B = -3, and C = -4.

Plugging these values into the quadratic formula:

x = (3 ± sqrt((-3)^2 - 4(1)(-4))) / (2(1))

x = (3 ± sqrt(9 + 16)) / 2

x = (3 ± sqrt(25)) / 2

x = (3 ± 5) / 2

Now, solve for x in both cases:

1. When using +5:
2. x = (3 + 5) / 2 = 8 / 2 = 4
3. When using -5:
4. x = (3 - 5) / 2 = -2 / 2 = -1

So, the roots of the quadratic equation x^2 - 3x - 4 = 0 are x = 4 and x = -1. Your substitution into the original quadratic equation to verify these roots is also correct:

At x = -1, (-1)^2 - 3(-1) - 4 = 1 + 3 - 4 = 0

At x = 4, (4)^2 - 3(4) - 4 = 16 - 12 - 4 = 0