Subject: Mathematics
Book: Maths Mastery
Polynomial inequalities like x²–5x+4≥0 require factoring to find critical points: (x–4)(x–1)≥0. Then test intervals around the roots x=1, x=4 to see where the product is nonnegative. Typically, you place the roots on a number line, check sign in intervals (–∞,1), (1,4), (4,∞), and choose intervals that satisfy ≥0. This approach extends to cubic or higher polynomials. In engineering or advanced math, polynomial inequalities define stability ranges or design constraints. Mastery ensures precise solutions to complex numeric intervals in real-life contexts.
If log(100) = 2 and log(10) = 1, what is log(1000)?
View QuestionIf a + b = 10 and ab = 21, what is the value of a^2 + b^2?
View QuestionIf the radius of a circle is 7 cm, what is its circumference?
View QuestionWhat is the value of log₃(27)?
View QuestionIf 5x - 2 = 13, what is the value of x?
View QuestionIf the sum of three consecutive integers is 72, what are the integers?
View QuestionThe perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?
View QuestionThe sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?
View QuestionIf two complementary angles differ by 30°, what are the angles?
View QuestionWhat is the length of the diagonal of a square with a side length of 7 cm?
View Question