Question 131609: I have to factor this problem and I have not found a solution for it.
8ksquared-19k+9 Found 2 solutions by 067isa, bucky:Answer by 067isa(13) (Show Source):
You can put this solution on YOUR website! 8k^2-19k+9 the AC is good way to do factoring
Ac= 8*9 = 72
so now we looking for two numbers the product of the is 72 and the sum is 19
factor out the 72 starting with one
72= 1.72 sum 73
2.36 38
3.24 27
4.18 22
6.12 18
8.9 17
not by AC method USe Quadritic formula this equation to double check
D= B^2-4AC = (19)^2-4(72)= 361 -288 = 73
x= (-b +- sqrt( b^2-4*a*c ))/(2*a)
x= -(-19)+-sqrt(73)/ 2(8)= 19 +sqrt(73)/ 16 and 19 - sqrt(73)/ 16 that it
You can put this solution on YOUR website! Given to factor:
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This does not factor very "nicely". The way to factor this is to use the quadratic equation.
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I'm going to presume that you know how to use the quadratic equation. When you have a quadratic
of the form you can find the solutions for k by using the quadratic formula:
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where a is the multiplier of the squared term (+8 in this problem), b is the multiplier of
the first degree term (-19 in this problem), and c is the constant term (+9 in this problem).
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If you substitute these values into the quadratic formula and simplify the resulting
equation for k you will find that k has two answers:
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k = 1.7215002 and k = 0.65349977
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This means that factors of the given problem include the two factors:
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But if you multiply these two factors together you get back to the equation:
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Notice that the left side ... which is equal to must be multiplied
by 8 to equal the original equation that we started with. Therefore, our equation is:
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So our factors of the original problem that you were given are:
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And if you multiply these all together you will get very, very close to the original expression.
You will be within the round-off error of the two decimal numbers.
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Hope this doesn't confuse you too much. If a quadratic expression is too difficult to
factor you can always use this general method. Use the quadratic formula to find the roots, then
convert the roots to the factor form, and finally multiply by an appropriate constant to make
the two factors work out to the original expression.
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Good luck with studying this to see how it works.
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