Algebra Errors

Question 1

Is (root82 + root82)^2 an integer?

Answer 1

Yes:

=82 + 2(root82)(root82) + 82

Question 2

How do you algebraically express “k is halfway between m and n on the number line”?

Answer 2

(m+n)/2=k

Question 3

What is the formula for the roots (x1 and x2) of equation ax^2 + bx + c = 0?

Answer 3

x1 + x2 = -b/a

AND

x1*x2 = c/a

Question 4

How do you maximize the product of two numbers when given their sum?

Eg. m^2 + p^2 < 100 -> what is the greatest possible value of mp?

Answer 4

The two numbers need to be equal.

Eg. m=p // 2m^2 < 100
m^2 < 50
m = 7 since m is a pos intg

Question 5

If a quadratic equation has integer coefficients only, and if one of the roots is a + rootb (where a and b are integers), then what is also a root of the equation?

Answer 5

a - rootb

Question 6

When can you cancel like terms from an equation with fractions?

Answer 6

When the like term to be canceled is non-zero

Question 7

If both x and y are not equal to 0, then what is always greater than the square root of (x+y)?

Answer 7

The square root of x + the square root of y

Question 8

When you have a linear relationship between two sets of numbers, how do you find the way in which they are related?

Answer 8

Find the increase/decrease ratio

Question 9

What is the only number that can be equal to its reciprocal?

Answer 9

1 and -1

Question 10

How can you re-express (n-3)! if you want to cancel terms?

Answer 10

(n-3)(n-4)!