An equation equivalent to the quadratic equation $\displaystyle x^{2}-6x+5=0$ is
- $\displaystyle 6x^{2}-5x+1=0$
- $\displaystyle x^{2}-5x+6=0$
- $\displaystyle 5x^{2}-6x+1=0$
- $\displaystyle \left | x-3 \right |=2$
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Correct answer
Explanation
The roots of x^2 - 6x + 5 = 0 are 1 and 5. The equation |x - 3| = 2 implies x - 3 = 2 or x - 3 = -2, so x = 5 or x = 1. These are equivalent.
AI explanation
To solve the quadratic equation x^2 - 6x + 5 = 0, we factor the quadratic to get (x - 1)(x - 5) = 0, yielding the roots x = 1 and x = 5. The absolute value equation |x - 3| = 2 produces two possible scenarios, which are x - 3 = 2 or x - 3 = -2. Solving these two simple equations gives the exact same roots, x = 5 and x = 1. Therefore, the equation |x - 3| = 2 is equivalent to the given quadratic equation.