Advanced MathVery hardSum of solutions of an exponential quadratic
Advanced Math practice question
The equation 3^(2x) − 10·3ˣ + 9 = 0 has two solutions. What is their sum?
Answer: 2
Let u = 3ˣ: u² − 10u + 9 = (u − 1)(u − 9) = 0, so 3ˣ = 1 or 3ˣ = 9, giving x = 0 or x = 2. The sum is 2.
Common wrong answers
- If you answered 3
- 3 adds x = 2 and x = 1 from misreading 3ˣ = 1 as x = 1.
- If you answered 9
- 9 is one value of u.
- If you answered 10
- 10 is the sum of the values of u, not of x.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.