Can someone tell me how to find k.
I don't want the answer - I want to know how I go about it otherwise it's pointless
Thanks
I don't want the answer - I want to know how I go about it otherwise it's pointless
Thanks
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see http://en.wikipedia.org/wiki/Quadratic_e…
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I suppose the obvious way would be to use the Quadratic Formula, because that 0.4 appears to make the factorisation difficult, but alternatively, 0.4 is just 2/5, so if you multiplied by 5 you would get 50k^2 + 15k - 2 = 0, and that will factorise OK.
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multiply all terms by 40
400k^2 + 120k − 16 = 0
leave the first two terms in the left hand side
400k^2 + 120k = 16
400k^2 is 20k squared
120k is twice the product of 20k by 3
LHS can easily become a perfect square adding 9
remember that 9 must be added to the RHS too
we get
400k^2 + 120k + 9 = 16 + 9
(20k + 3)^2 = 25
20k + 3 = ± 5
20k = - 3 ± 5
k = (- 3 ± 5)/20
k₁ = (- 3 - 5)/20 = -8/20 = -2/5
k₂ = (- 3 + 5)/20 = 2/20 = 1/10
hope it is useful
400k^2 + 120k − 16 = 0
leave the first two terms in the left hand side
400k^2 + 120k = 16
400k^2 is 20k squared
120k is twice the product of 20k by 3
LHS can easily become a perfect square adding 9
remember that 9 must be added to the RHS too
we get
400k^2 + 120k + 9 = 16 + 9
(20k + 3)^2 = 25
20k + 3 = ± 5
20k = - 3 ± 5
k = (- 3 ± 5)/20
k₁ = (- 3 - 5)/20 = -8/20 = -2/5
k₂ = (- 3 + 5)/20 = 2/20 = 1/10
hope it is useful
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{k= -0.4}, {k = 0.1}
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You could use the quadratic formula