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anonymous
 one year ago
One of the roots of the equation
x^2+Kx−6=0
is 3 and K is a constant.
Which one is greater
a. The value of K
b. 1
anonymous
 one year ago
One of the roots of the equation x^2+Kx−6=0 is 3 and K is a constant. Which one is greater a. The value of K b. 1

This Question is Closed

phi
 one year ago
Best ResponseYou've already chosen the best response.1one of the roots is 3 that means x=3 or , adding 3 to both sides, x3=0 let the other root be called "a" then we know (x3)(xa)=0 multiply that out x^2 3xax +3a = 0 or x^2 (3+a) x + 3a =0

phi
 one year ago
Best ResponseYou've already chosen the best response.1match up x^2 (3+a) x + 3a =0 x^2+Kx−6=0 we see 3a= 6 solve for a by dividing both sides by 3 we get a= 2

phi
 one year ago
Best ResponseYou've already chosen the best response.1using a= 2 in x^2 (3+a) x + 3a =0 x^2 (32) x +3*2 = 0 simplifying: x^2  (1) x 6 =0 or x^2 x 6 =0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why is one of the roots 3?

phi
 one year ago
Best ResponseYou've already chosen the best response.1It says One of the roots of the equation x^2+Kx−6=0 is 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hey how do i know if it's (x3)(xa) and not (x+a) ?????????

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tried (x3)(+a) and it worked out better

phi
 one year ago
Best ResponseYou've already chosen the best response.1say you factored a quadratic and got (x3)(x2) = 0 the roots are the x values that make this expression zero. this will be zero if x=3 (which makes 33 zero) or x=2 (which makes 22 zero) if you had (x3) (x+2)=0 the second root is when x= 2 notice if we write (x+2) as (x  (2)) the number 2 is the root. in other words, if we write (xa) then a will be the root (the x value that makes the expression zero)

phi
 one year ago
Best ResponseYou've already chosen the best response.1btw, what is question ? It looks like it was cut off at the top.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's asking which one is greater a or b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so in what cases would it be (x3) (x+a)

phi
 one year ago
Best ResponseYou've already chosen the best response.1in this case , K = 1, so they are equal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm still having a hard time understanding how I would know for sure that it would be ()() instead of ()(+) or (+)()

phi
 one year ago
Best ResponseYou've already chosen the best response.1Let's factor x^2 x 6 =0 the 6 means 1) different signs on the roots, 2) they multiply to give us 6 1,6 2,3 are the choices the 1x means the larger nuumber is negative, and they add to 1 so 2 and 3 are the factors (x+2)(x3)=0 or (x  (2)) (x3) = 0

phi
 one year ago
Best ResponseYou've already chosen the best response.1I guess the point is you can always write the factors as (x  a) where a is the root. if the root were 2 x= 2 makes the expression zero, then the factor would be (x 2) (which is the same as (x+2) )

phi
 one year ago
Best ResponseYou've already chosen the best response.1But I think I am being a clear as mud here.
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