X²-8x-240 This is very confusing?

Question

Ok now this is really confusing I cant find anything big enough that equals 8 when added together that equals 240 when multiplied?

Answer 1

Use quadratic formula, then pretend using factorization.

Question Number 1 :

For this equation x^2 - 8*x - 240 = 0 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use factorization to find the root of the equation !

Answer Number 1 :

The equation x^2 - 8*x - 240 = 0 is already in a*x^2+b*x+c=0 form.

By matching the constant position, we can derive that the value of a = 1, b = -8, c = -240.

1A. Find the roots using Quadratic Formula !

  Remember the formula,

    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  As we know that a = 1, b = -8 and c = -240,

  we just need to subtitute the value of a,b and c in the abc formula.

  Which produce x1 = (-(-8) + sqrt( (-8)^2 - 4 * (1)*(-240)))/(2*1) and x2 = (-(-8) - sqrt( (-8)^2 - 4 * (1)*(-240)))/(2*1)

  Which make x1 = ( 8 + sqrt( 64+960))/(2) and x2 = ( 8 - sqrt( 64+960))/(2)

  Which can be turned into x1 = ( 8 + sqrt( 1024))/(2) and x2 = ( 8 - sqrt( 1024))/(2)

  We got x1 = ( 8 + 32 )/(2) and x2 = ( 8 - 32 )/(2)

  We get following answers x1 = 20 and x2 = -12

1B. Use factorization to find the root of the equation !

  x^2 - 8*x - 240 = 0

  ( x - 20 ) * ( x + 12 ) = 0

  So we got the answers as x1 = 20 and x2 = -12

Answer 2

Try this one:

x^2 - 8x - 240 = (x-20)(x+12)

Answer 3

Then values are 12 and -20.

(x-20)(x+12)

Answer 4

x^2-8x-240

( x-20)(x+12)

key is to find factors of 240 and see which one wou;d equal 8 and dont forget because it is a negative 240 one of the numbers will be negative

Answer 5

-20 and 12 add up to -8

x²-8x-240

(x - 20)(x + 12)