How do you solve #0 = x^2 - 5x + 6# using the quadratic formula?

Answer 1

#x=3,2#

#color(blue)(0=x^2-5x+6#

Rewrite in standard form

#rarrcolor(purple)(x^2-5x+6=0#
This is a Quadratic equation (in form #ax^2+bx+c=0#)

Use Quadratic formula

#color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)#
Remember that #a,bandc# are the coefficients of #x^2,xand6#

Now,

#color(red)(a=1,b=-5,c=6#
#rarrx=(-(-5)+-sqrt(-5^2-4(1)(6)))/(2(1))#
#rarrx=(5+-sqrt(-5^2-4(1)(6)))/(2)#
#rarrx=(5+-sqrt(25-4(1)(6)))/(2)#
#rarrx=(5+-sqrt(25-(24)))/(2)#
#rarrx=(5+-sqrt(1))/(2)#
#rarrx=(5+-1)/(2)#
Now we have #2# solutions for #x#
#color(purple)(x=(5+1)/(2)=6/2=3#
#color(orange)(x=(5-1)/(2)=4/2=2#
#color(blue)( :.ul bar| x=2,3|#
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Answer 2

To solve (0 = x^2 - 5x + 6) using the quadratic formula, which is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}) for the quadratic equation (ax^2 + bx + c = 0), first identify (a), (b), and (c) from the given equation.

In this case, (a = 1), (b = -5), and (c = 6).

Now, substitute these values into the formula:

(x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 6}}{2 \cdot 1})

(x = \frac{5 \pm \sqrt{25 - 24}}{2})

(x = \frac{5 \pm \sqrt{1}}{2})

Since the square root of 1 is 1, this simplifies to:

(x = \frac{5 \pm 1}{2})

So, the two solutions are:

(x = \frac{5 + 1}{2} = \frac{6}{2} = 3)

and

(x = \frac{5 - 1}{2} = \frac{4}{2} = 2)

Therefore, the solutions to (0 = x^2 - 5x + 6) are (x = 3) and (x = 2).

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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.

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.

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.

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.

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