Hi, I have a problem with these:
1. If the roots of 2x^2-kx+14=0 are integers, then which of the following could be the value of constant k?
a. 6
b. 8
c. 10
d. 12
e. 16
I know that I should use 'sum of the roots' and 'product of the roots', yet I can't solve it. I don't know why an explanation in the book says that sum of the roots (r1+r2= k/2), and the product (r1r2=14/2=7) imply that the possible roots are either {7,1} or {-7,-1}. It also says that it implies that k=16 or -16.
Absolute value problem:
2. If x + sqrt( (1-sqrt(3))^2 ) = 3, then x=. Yes, I know it's gibberish.
a. 1 - sqrt(3)
b. 4 - sqrt(3)
c. 2 + sqrt(3)
d. sqrt(3) -2
e. sqrt(3) -4
My solution:
1) sqrt( (1-sqrt(3))^2 ) = 3 - x
2) |1 - sqrt(3)| = 3 - x At this moment I'm stuck, because I don't want to use calculator in order to keep sqrt(3).
Thank you!
1. If the roots of 2x^2-kx+14=0 are integers, then which of the following could be the value of constant k?
a. 6
b. 8
c. 10
d. 12
e. 16
I know that I should use 'sum of the roots' and 'product of the roots', yet I can't solve it. I don't know why an explanation in the book says that sum of the roots (r1+r2= k/2), and the product (r1r2=14/2=7) imply that the possible roots are either {7,1} or {-7,-1}. It also says that it implies that k=16 or -16.
Absolute value problem:
2. If x + sqrt( (1-sqrt(3))^2 ) = 3, then x=. Yes, I know it's gibberish.
a. 1 - sqrt(3)
b. 4 - sqrt(3)
c. 2 + sqrt(3)
d. sqrt(3) -2
e. sqrt(3) -4
My solution:
1) sqrt( (1-sqrt(3))^2 ) = 3 - x
2) |1 - sqrt(3)| = 3 - x At this moment I'm stuck, because I don't want to use calculator in order to keep sqrt(3).
Thank you!