−x^2 + bx−67 6 = 0 In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b?
Correct answer: 51 (parsed from the explanation — this source omits an answer key for this item)
Explanation
2 + + = The correct answer is 51. A quadratic equation of the form ax bx c 0, where a, b, and c are constants, has no real solution if and only if its discriminant, - 2+ =- =- 4ac b , is negative. In the given equation, a 1 and c 676. Substituting - - 1 for a and 676 for c in this expression yields a discriminant of 2 -( -)( - ) 2- b 4 1 676 , or b 2,704. Since this value must be negative, 2 - < 2< b 2,704 0, or b 2,704. Taking the positive square root of each side of this < inequality yields b 52. Since b is a positive integer, and the greatest integer less than 52 is 51, the greatest possible value of b is 51.
Loading…
Searched on YouTube by topic, not by question text. Open this search on YouTube →
Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.