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# How to find the values of the constants k and c?

I'm find this question hard to work out. Please can someone help me? :)

You are given f(x) = x^2 + kx + c. Given also that f(2)=0 and f(-3)=35, find the values of the constants k and c.

Thank you very much :)

### 3 Answers

- DouglasLv 77 years agoFavorite Answer
f(2) = 2² + k(2) + c = 0

f(-3) = -3² + k(-3) + c = 35

Drop the functions on the left and multiply the squares:

4 + k(2) + c = 0

9 + k(-3) + c = 35

Move all the constants to the right:

2k + c = -4

-3k + c = 26

Eliminate c by subtracting the first equation from the second:

-5k = 30

k = -6

Now one can use either equation to find c I will use the first:

f(2) = 2² - 6(2) + c = 0

4 - 12 + c = 0

-8 + c = 0

c = 8

Check:

2² - 6(2) + 8 = 0

-3² - 6(-3) + 8 = 35

4 - 12 + 8 = 0

9 + 18 + 8 = 35

-8 + 8 = 0

27 + 8 = 35

0 = 0

35 = 35

This checks. k = -6 and c = 8

- 7 years ago
Put x=2 in the equation-

(2)^2 + k(2) + c = 0

4 + 2k + c = 0

Put x=-3 in the equation-

(-3)^2 + k(-3) + c = 35

9 - 3k + c = 35

Thus you got two variables and two equations.

Find out the variables yourself...

- 7 years ago
f(x) = x^2 + kx +c

now, f(2) =0 means put x=2

2^2 + 2k +c =0

4+2k +c=0

2k +c = -4 .......(i)

f(-3) = 35

(-3)^2 -3k + c= 35

9 - 3k + c =35

-3k + c= 26 ....(ii)

solve eqn (i) and (ii)

-3k + c= 26 ...(ii)

2k + c = -4 ...(i)

___________ subtract (i) from (ii)

-5k +0 = 30

k= -30/5 = -6

__________

put value of k in (i)

2(-6) + c = -4

-12 + c = - 4

c = -4 + 12

c = 8