Advanced MathVery hardConstant for a single real solution
Advanced Math practice question
For what value of the constant c does the equation 2x² + 8x + c = 0 have exactly one real solution?
Answer: 8
One real solution means the discriminant is zero: 8² − 4(2)(c) = 64 − 8c = 0, so c = 8. (Then 2x² + 8x + 8 = 2(x + 2)².)
Common wrong answers
- If you answered 4
- 4 is c/2 or the number inside (x + 2)² squared; the equation's c is 8.
- If you answered 16
- 16 forgets the coefficient 2 in 4ac: 64 − 4c = 0 gives 16, but the x² coefficient is 2.
- If you answered 64
- 64 is b², not c.
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.