How can you solve #x^2 – 4x – 5 = 0# by using the quadratic formula and by factoring?

Question

How can you solve  #x^2 – 4x – 5 = 0# by using the quadratic formula and by factoring?

Julia Adams · Accepted Answer

Solve x^2 - 4x - 5 = 0

Ans: -1 and 5

y = x^2 - 4x - 5 = 0 Since (a - b + c = 0), use Shortcut. The 2 real roots are: - 1 and (-c/a = 5)

Eli Assouline · Answer

undefined To solve the equation $x^2 - 4x - 5 = 0$ using the quadratic formula:

1. Identify coefficients a, b, and c from the quadratic equation $ax^2 + bx + c = 0$.
2. Apply the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$.
3. Substitute the values of a, b, and c into the quadratic formula.
4. Calculate the discriminant ($b^2 - 4ac$).
5. If the discriminant is positive, there are two real solutions; if it's zero, there's one real solution; if it's negative, there are two complex solutions.
6. Plug the values of the discriminant, a, b, and c into the quadratic formula and solve for x.

To solve the equation $x^2 - 4x - 5 = 0$ by factoring:

1. Write the quadratic equation in the form $ax^2 + bx + c = 0$.
2. Factor the quadratic expression into two binomials.
3. Set each binomial equal to zero and solve for x.
4. The solutions obtained are the roots of the quadratic equation.