ALGEBRA 2 FUNCTION PROBLEM-10pts to anyone that can explain and show an answer!?

Question

ALGEBRA 2 FUNCTION PROBLEM-10pts to anyone that can explain and show an answer!?
ALGEBRA 2 FUNCTION PROBLEM-10pts to anyone that can explain and show an answer!?
Given f(x)=2x^2+5x-k, find k when one of the roots is equal to 1/2
the answer is 3, but i don't know how my teacher got it!
THANKS!!!!!!

Answer 1

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A root, also called a 'zero', of a function is a value for x that makes the function go to 0.

So, saying that ½ is a root of f(x)=2x²+5x-k tells you that f(½)=0 so that:



                                                    f(x)  =    2x²   +  5x  -  k

                                                   f(½) = 2(½)²+5(½)-k = 0

                                                                    2(¼)+⁵∕₂-k = 0

                                                                         ½+⁵∕₂-k = 0

                                                                                3-k = 0

                                                                                   3 = k           ← ANSWER



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Answer 2

The funtion is equal to 0

Plug 1/2 into the only root in the equation.

It would be harder if there were multiple roots, but luckily you only have the one x^2

Answer 3

2x² + 5x – ok factors into (2x + a)(x + b), with ab = -ok and a + 2b = ok, so if b = -a million/2, then (2x + a)(x – ½) = 2x² + (a – a million)x – ½a = 2x² + 5x – ok which makes a – a million = 5, so a = 6, and -½(6) = -3 = -ok, so ok = 3 checking, 2x² + 5x – 3 = (2x - a million)(x + 3)