Mathematics

Question

1.What are the zeros of the polynomial function?
f(x)=x^2+9x+20

2.What are the zeros of the polynomial function?

f(x)=x^2−4x−60


3.What are the roots of the equation?

x^2+24=14x


4.What are the zeros of the function?

g(x)=x^2−x−72

1 Answer

  • Let's to the first example:

    f(x) = x^2 + 9x + 20

    Ussing the formula of basckara

    a = 1
    b = 9
    c = 20

    Delta = b^2 - 4ac

    Delta = 9^2 - 4.(1).(20)

    Delta = 81 - 80

    Delta = 1

    x = [ -b +/- √(Delta) ]/2a

    Replacing the data:

    x = [ -9 +/- √1 ]/2

    x' = (-9 -1)/2 <=> - 5

    Or

    x" = (-9+1)/2 <=> - 4
    _______________

    Already the second example:

    f(x) = x^2 -4x -60

    Ussing the formula of basckara again

    a = 1
    b = -4
    c = -60

    Delta = b^2 -4ac

    Delta = (-4)^2 -4.(1).(-60)

    Delta = 16 + 240

    Delta = 256

    Then, following:

    x = [ -b +/- √(Delta)]/2a

    Replacing the information

    x = [ -(-4) +/- √256 ]/2

    x = [ 4 +/- 16]/2

    x' = (4-16)/2 <=> -6

    Or

    x" = (4+16)/2 <=> 10
    ______________

    Now we are going to the 3 example

    x^2 + 24 = 14x

    Isolating 14x , but changing the sinal positive to negative

    x^2 - 14x + 24 = 0

    Now we can to apply the formula of basckara

    a = 1
    b = -14
    c = 24

    Delta = b^2 -4ac

    Delta = (-14)^2 -4.(1).(24)

    Delta = 196 - 96

    Delta = 100

    Then we stayed with:

    x = [ -b +/- √Delta ]/2a

    x = [ -(-14) +/- √100 ]/2

    We wiil have two possibilities

    x' = ( 14 -10)/2 <=> 2

    Or

    x" = (14 +10)/2 <=> 12
    ________________


    To the last example will be the same thing.

    f(x) = x^2 - x -72

    a = 1
    b = -1
    c = -72

    Delta = b^2 -4ac

    Delta = (-1)^2 -4(1).(-72)

    Delta = 1 + 288

    Delta = 289

    Then we are going to stay:

    x = [ -b +/- √Delta]/2a

    x = [ -(-1) +/- √289]/2

    x = ( 1 +/- 17)/2

    We will have two roots

    That's :

    x = (1 - 17)/2 <=> -8

    Or

    x = (1+17)/2 <=> 9


    Well, this would be your answers.


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