What's a quick method to solve the problem below (other than plugging in)?
7. If one root of the equation 2x2 + 3x – k = 0 is 6, what is the value of k?
(A) 90
(B) 42
(C) 18
(D) 10
(E) –10
OA is E
quick method to solve this
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I get A
2x^2 + 3x – k = 0 ---> dividing by 2 ---> x^2 + 3/2x - k/2 = 0
this can be factorize as (x+a)(x+b) where
a * b = -k/2
a + b = 3/2
we know that one of the solutions is x = 6 so a = -6 or b = -6
a + b = 3/2 --> -6 + b = 3/2 ---> b = 15/2
-6 * 15/2 = - K/2 ---> 6 * 15 = K ---> K = 90
2x^2 + 3x – k = 0 ---> dividing by 2 ---> x^2 + 3/2x - k/2 = 0
this can be factorize as (x+a)(x+b) where
a * b = -k/2
a + b = 3/2
we know that one of the solutions is x = 6 so a = -6 or b = -6
a + b = 3/2 --> -6 + b = 3/2 ---> b = 15/2
-6 * 15/2 = - K/2 ---> 6 * 15 = K ---> K = 90
- ssmiles08
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One way I found useful is that k must be divisible by 6, so that eliminates D and E.
I wrote the factored form out so it would be better so see:
(2x + ?)(x - 6) = 0
x has to be in the (x-6) because one of the values for x = 6 so -6 and +6 would add up to produce zero.
From there we can see that 15 fits in perfectly because it gives us the +3x value.
I wrote the factored form out so it would be better so see:
(2x + ?)(x - 6) = 0
x has to be in the (x-6) because one of the values for x = 6 so -6 and +6 would add up to produce zero.
From there we can see that 15 fits in perfectly because it gives us the +3x value.
Test for which of the answer choices this is a perfect squareoks wrote:What's a quick method to solve the problem below (other than plugging in)?
7. If one root of the equation 2x2 + 3x – k = 0 is 6, what is the value of k?
(A) 90
(B) 42
(C) 18
(D) 10
(E) –10
OA is E
(b^2 -4ac)^.5=(9+8k)^.5 =(729)^.5=27. First test reveals answer
Choose A. Handy to know first 30 roots.