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How do you solve #x^2 - 5x+ 6 = 0#?

Answer 1

Eva Abramson

#color(blue)(x=2 or x=3)#

Given:

#x^2-5x+6=0#

Step.1

Consider

#y = f(x) = x^2-5x+6=0#

Split the middle term of the Quadratic Expression:

#x^2-3x-2x+6=0#

We can rewrite this in factor form:

#x(x-3)-2(x-3) = 0#

Hence,

the factors are: #(x-3) and (x-2)#

This would mean

either #(x-3) = 0 or (x-2) = 0#

Now we can write our solutions as

#color(blue)(x=2 or x=3)#

We can also graph our quadratic to verify our solutions

We analyze the graph and note the following:

x-intercepts are: #(2,0), (3,0)#

Hence, our solutions are verified.

Some additional pieces of useful information for you:

Vertex is at #(2.5, -0.25)#

And,

Axis of Symmetry is at #x = 2.5#

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Answer 2

Julia Adams

To solve the quadratic equation (x^2 - 5x + 6 = 0), you can use the factoring method or the quadratic formula. Factoring method: Factor the quadratic expression into two binomials and set each binomial equal to zero. Quadratic formula: Use the formula (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}), where (a), (b), and (c) are the coefficients of the quadratic equation. Substituting the values into the formula will give you the solutions for (x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.