SOLUTION: What should be the value of k in 2x^4-5x^2+k so that x-5 is a zero? I kinda don't know how to solve this one may I please ask for your assistance, I would be very happy if you c

Question 1168460: What should be the value of k in 2x^4-5x^2+k so that x-5 is a zero?
I kinda don't know how to solve this one may I please ask for your assistance, I would be very happy if you could help me out
Found 3 solutions by josgarithmetic, Theo, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
x-5 is a zero, or x-5 is one of the factors of 2x^4-5x^2+k;

If x-5 is a facotr then same as saying 5 is a root.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if x - 5 is a zero, then solve for x to get = 5
set the equation equal to 0 and replace x with 5 in the equation to get:

2x^4 - 5x^2 + k = 0 becomes:

2*5^4 - 5*5^2 + k = 0 which becomes:

1125 + k = 0

solve for k to get:

k = -1125

the equation becomes 2x^4 - 5x^2 - 1125 = y

when you replace x with 5, you get y = 0.

the graph of this equation looks like this.

it actually has 2 zeroes, one at x = -5 and one at x = 5.

it actually has 4 roots, except that 2 of them aren't real and so don't show up on the graph.

the 2 roots that are real are the zeroes.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

                    In a very short form

For this problem, and for many other similar problems, the method of solution is

to substitute the given value of the root into the polynomial and to equate the obtained expression to zero

        ( because it is the root (!) ).

                    MEMORIZE this method (!)

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