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Question 162786: x^2+10=0 this is solve by factoring, and the second problem is 2x6^2-3x-2=0
f(x)= 2x^2-7x+3 find f(2).Can you please work the problems out so that I see how to work them out so I can do other problems. Thank you.
Found 2 solutions by eperette, gonzo:
Answer by eperette(173)   (Show Source):
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! some formulas:
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general form for a quadratic equation is 
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general form for the quadratic formula is  and 
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general form for the factors of a quadratic equation are 
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it doesn't appear that the first equation will provide real solutions.
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x^2 + 10 = 0
x^2 = -10
x = +/- sqrt(-10)
looks like the answer will not be a real number.
looking at the general form of a quadratic equation, it looks like
a = 1, b = 0, c = 10 for the equation x^2 + 10 = 0.
using the part of the quadratic formula under the square root,
 becomes  becomes  which indicates no real solution.
not sure what you got but if the solution has to be real, there is no solution for the first one.
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i don't understand your second problem.
2x6^2-3x-2 doesn't make sense.
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if it's 2x^2-3x-2, then we can find a solution.
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here's how i would do it.
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i would look at 2x^2-3x-2 and note the following:
a = 2
b = -3
c = -2
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since c is negative, my solution will look like (x-something) * (x+something)
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what factors will allow me to get c = -2?
possible factors are -1, 1, -2, 2.
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what factors will allow me to get a = 2?
possible factors are 1, 2.
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now i need combinations of a factors and c factors that will add up to -3
my possible factors are -1, 1, -2, 2 for c, and 1, 2 for a.
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1 - 4 = -3 looks like it's the only possible combination that would do it.
i would get -4 by multiplying -2 * 2
i would get 1 by multiplying 1 * 1
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first a definition of FOIL.
FOIL means First, Outer, Inner, Last.
it means multiply your first terms together first, then your outer terms together next, then your inner terms together next, then your last terms next. add them all up and you get your equation.
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if your factors are (a1x + c1) * (a2x + c2), then
F = First = a1x * a2x.
O = Outer = a1x * c2
I = Inner = a2x * c1
L = Last = c1 * c2
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add them up together and you get
a1x*a2x + a1x*c2 + a2x*c1 + c1*c2 = 0
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one of the Inner Factors has to be -4, and the other one has to be 1.
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in order for an inner or outer factor to be -4, i need (2*x * -2)
in order for an inner or outer factor to be 1, i need (x * 1)
factors of (2*x + 1) * (x - 2) should do it.
inner factors are 1*x = 1x
outer factors are 2*x*-2 = -4*x = -4x
-4x + x = -3x
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factors look like they are (2*x + 1) * (x - 2)
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using FOIL, that equals 2x^2 + x - 4x -2 = 2x^2 -3x -2 which is good.
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solution is (2*x+1) * (x-2) = 0.
x = -1/2 or x = 2.
one or both could work.
at least one has to work or the solution is no good.
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substituting x = 2 in the original equation gets
2*2^2 - 3*2 - 2 = 8 - 6 - 2 = 0
x = 2 works.
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substituting x = -1/2 in the original equation gets
2*(-1/2)^2 - 3*(-1/2) - 2 = 0
which becomes
2*(1/4) - 3*(-1/2) - 2 = 0
multiply both sides of the equation by 4 to remove the denominators and the equation becomes
2 - (-3*2) - 8 = 0
2 - (-6) - 8 = 0
2 + 6 - 8 = 0
x = -1/2 works also.
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if you can't spot the solution right away, then go to the quadratic formula. it will provide you with the solution, if there is one.
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general form for a quadratic equation is
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general form for the quadratic formula is and
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since your equation is 2^x^2 - 3*x -2
a = 2
b = -3
c = -2
just substitute these values in the quadratic formula and solve.
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your last request is to find f(2) from the equation
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this is just a matter of substititon.
you replace x with 2 and solve the equation.
the equation becomes
2*2^2 - 7*2 + 3
which becomes
2*4 - 14 + 3
which becomes
8 - 14 + 3
which becomes
-3
f(2) = -3
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