Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

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

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  • 7 years ago
    Favorite 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

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