Advanced MathVery hardQuartic equation that is quadratic in x²
Advanced Math practice question
What is the sum of the positive solutions of x⁴ − 13x² + 36 = 0?
Answer: 5
Let u = x²: u² − 13u + 36 = 0 → (u − 4)(u − 9) = 0 → x² = 4 or x² = 9. The positive solutions are 2 and 3, whose sum is 5.
Common wrong answers
- If you answered 0
- 0 is the sum of all four solutions (±2, ±3).
- If you answered 6
- 6 is 2 × 3, the product.
- If you answered 13
- 13 is the sum of x² values (4 + 9), not of x values.
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.