Solve the Quadratic Equation: x² - 2x - 3 = 0

Question

x2−2x−3=0 x^2-2x-3=0

Video Solution

Solution Steps

00:00 Find X
00:03 We'll break it down using trinomials, let's look at the coefficients
00:08 We want to find 2 numbers whose sum equals B (-2)
00:16 and their product equals C (-3)
00:22 These are the matching numbers, let's substitute in parentheses
00:33 Let's find what zeros each factor
00:43 And this is the solution to the question

Step-by-Step Solution

Let's observe that the given equation:

x2−2x−3=0 x^2-2x-3=0 is a quadratic equation that can be solved using quick factoring:

x2−2x−3=0⟷{?‾⋅?‾=−3?‾+?‾=−2↓(x−3)(x+1)=0 x^2-2x-3=0 \longleftrightarrow\begin{cases}\underline{?}\cdot\underline{?}=-3\\ \underline{?}+\underline{?}=-2\end{cases}\\ \downarrow\\ (x-3)(x+1)=0 and therefore we get two simpler equations from which we can extract the solution:

(x−3)(x+1)=0↓x−3=0→x=3x+1=0→x=−1x=−1,3 (x-3)(x+1)=0 \\ \downarrow\\ x-3=0\rightarrow\boxed{x=3}\\ x+1=0\rightarrow\boxed{x=-1}\\ \boxed{x=-1,3} Therefore, the correct answer is answer B.

Answer

x=3,x=−1 x=3,x=-1

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Related Subjects

Factoring Trinomials Factorization

Question Types

Factoring Trinomials: Solving the problem