Solve the Quadratic Equation: x²-7x+12=0 Step by Step

Question

x2−7x+12=0 x^2-7x+12=0

Video Solution

Solution Steps

00:00 Find X
00:03 We'll break it down using trinomial, we'll look at the coefficients
00:08 We want to find 2 numbers whose sum equals B (-7)
00:15 and their product equals C (12)
00:23 These are the matching numbers, we'll substitute in parentheses
00:33 We'll 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:

x2−7x+12=0 x^2-7x+12=0 is a quadratic equation that can be solved using quick factoring:

x2−7x+12=0⟷{?‾⋅?‾=12?‾+?‾=−7↓(x−3)(x−4)=0 x^2-7x+12=0 \longleftrightarrow\begin{cases}\underline{?}\cdot\underline{?}=12\\ \underline{?}+\underline{?}=-7\end{cases}\\ \downarrow\\ (x-3)(x-4)=0 and therefore we get two simpler equations from which we can extract the solution:

(x−3)(x−4)=0↓x−3=0→x=3x−4=0→x=4x=3,4 (x-3)(x-4)=0 \\ \downarrow\\ x-3=0\rightarrow\boxed{x=3}\\ x-4=0\rightarrow\boxed{x=4}\\ \boxed{x=3,4} Therefore, the correct answer is answer A.

Answer

x=3,x=4 x=3,x=4

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