Discriminant
How many real roots does x^2 - x + 2 have?
0
How many positive factors does 144 have?
15
If f(x + 1) = x^2, what does f(x) equal?
f(x) = (x - 1)^2
What is the sum of the roots of x^2 + 59x - 67?
-59
How many positive integers from 1 to 100 (inclusive) are divisible by 3 but not by 2?
17
How many positive integer values of c make the equation x^2 - 4x + c have exactly 2 roots?
3
(These are 1, 2 and 3)
How many even factors does the number 240 have?
16
Alex creates a function f(x) such that f(3x) = 1/x. Help Alex find f(x) in simplest terms.
3/x
If x^2 + 9x - 4 has roots r and s, what is r^2 + s^2?
85
What is the sum of the exterior angles of a nonagon (9 sided shape)?
360 deg
If ax^2 + 6x + c has 1 root, and a and c are positive integers, how many possible values are there for c?
3
A positive integer has exactly 16 positive factors. 2 of those factors are 12 and 15. What is that number?
120
If f(2x + 3) = 3x^2, find the leading coefficient of f(7x).
147/4
If ax^2 + 9x + 45 has roots r and s, what is rs/(r + s)?
-5
How many ways can you choose 2 different items from a set of 6 different items? (order doesn’t matter)
15
Say that ax^2 + bx + 2a + 2b and 2ax^2 + 2bx^2 + ax + b both have two roots each. a^2 + b^2 is greater than what value?
2
If a + ab + b = 7 how many solution pairs exist where a > b?
2
If f(0.1x) + f(0.2x) = 6x^2 and f(0.5) = 50, what is f(2)?
500
For equation 10x^2 - bx - c, let p be the product of the roots and s be the sum of the roots. Given that ps an integer and that 0 < bc < 100 how many integer values b are possible?
0
Given that x - y = 1 and x^2 + y^2 = 7, find x^3 - y^3.
10
Let x^2/n - 6x + c and x^2/m + 14x + c both have one root each. Given that n is a positive integer, m is a positive multiple of at LEAST what real number?
(3/7)^2 or 9/49
How many positive factors of 210^2 are indivisible by any perfect square greater than 1?
16
Include 1!
If f(x + 2x + 3x + … + nx) = (n + 1)x, and f(x) is a positive integer for any valid input x, x must be a positive multiple of at LEAST what expression in terms of n?
n/2
Letting r and s be the roots in equation nx^2 + 96x - 320, how many integer values n make both rs and r + s integers?
12
What is the sum of ALL solutions to the equation (x^11)/17 = 23?
0
Roots of unity :)