Advanced MathVery hardDiscriminant and number of real solutions
Advanced Math practice question
For which value of c does the equation x² + 6x + c = 0 have exactly one real solution?
- A. 9Correct
- B. 6
- C. −9
- D. 3
Answer: A. 9
One real solution means discriminant 0: 36 − 4c = 0, so c = 9. (Then (x + 3)² = 0.)
Why the other answers are wrong
- B. 6
- c = 6 gives discriminant 36 − 24 = 12 > 0: two solutions.
- C. −9
- c = −9 gives 36 + 36 = 72 > 0: two solutions.
- D. 3
- c = 3 gives 36 − 12 = 24 > 0: two solutions.
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.