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# Help needed (Urgent)

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If $$x^2$$$$-3x+2 = (x-k)^2+p$$, what is the value of $$p$$?

a.) None of the below

$$b.) 2$$

$$c.) -2$$

$$d.) -1/4$$

$$e.) 1$$

Apr 29, 2022

#1
+148
+3

Classic complete the square problem ^_^

If you expand the right side, we have

$$x^2 - 3x + 2 = x^2 - 2kx + k^2 + p$$.

Because like terms have to match on both sides, we garner $$-3x = -2kx \implies k = \frac{3}{2}$$.

Now, we need $$2 = k^2 + p.$$ Substituting the value for $$k$$ we just found, we get $$2 = \left(\frac{3}{2}\right)^2 + p \implies 2 = \frac{9}{4} \implies p = -1/4$$.

So, we can conclude the answer $$d.) -1/4$$.

Apr 29, 2022

#1
+148
+3

Classic complete the square problem ^_^

If you expand the right side, we have

$$x^2 - 3x + 2 = x^2 - 2kx + k^2 + p$$.

Because like terms have to match on both sides, we garner $$-3x = -2kx \implies k = \frac{3}{2}$$.

Now, we need $$2 = k^2 + p.$$ Substituting the value for $$k$$ we just found, we get $$2 = \left(\frac{3}{2}\right)^2 + p \implies 2 = \frac{9}{4} \implies p = -1/4$$.

So, we can conclude the answer $$d.) -1/4$$.

Anthrax Apr 29, 2022
#2
+124696
+1

Nice, Anthrax  !!!!

CPhill  Apr 29, 2022