Tham khảo tài liệu 'sat ii math episode 1 part 3', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Math Review Illustrative Problems and Solutions 35 10. If two roots of the equation X3 ax2 bx c 0 with a b and c integers are 1 and 2 - 3i find the value of a. Solution Another root must be 2 3i. Sum of the roots -a l 2 3z 2-3z -a a -5 11. Solve the equation y2 for X in terms of y. x 2 Solution X xy2 - 2y2 2 y xy X 12. How many roots does the equation y x 6 -X have Solution -A I V -A X2 X - 6 0 x-3 x 2 0 X 3 X -2 Check X 3 5 9 -3 does not check Check X -2 5 4 2 does check There is one root. 8. Inequalities The following principles are important in solving problems dealing with inequalities. 1. For all real values ofp q and r ifp q then p r q r. 2. For all real values ofp q r r 0 ifp q thenpr qr for values of r 0 andpr qr for values of r 0. 3. If x a then -a X a. 4. The sum of the lengths of two sides of a triangle is greater than the length of the third side. 5. If two sides of a triangle have unequal measure the angles opposite have unequal measure and the angle with greater measure lies opposite the longer side and conversely. In solving quadratic inequalities or trigonometric inequalities a graphic approach is often desirable. ARCO SAT II Math arco 36 Part III Illustrative Problems 1. Find the solution set of the inequality 8y - 5 4y 3. Solution Subtract 4y from both sides and add 5. 8y-4y 5 3 4y 8 y 2 2. Find the solution set of the inequality x 3 5. Solution When x 3 0 x 3 x 3 x 3 5 X 2 When x 3 0 x 3 - x 3 - x 3 5 X 3 -5 X -8 The solution set consists of 1 interval - 8 x 2. 3. In APQR PQ PR 5 and 60 m 4 P 90 . What is the possible range of values of QR Solution When mẶ P 60 PQR is equilateral and QR 5. When mẶ P 90 PQR is right isosceles and QR 5 V2. 5 QR 5 72 arco ARCO SAT II Math Math Review Illustrative Problems and Solutions 37 Solution 4. For what values of x between 0 and 360 is sin x cos x Graph the two functions on the same set of axes. Solution Solution Solution From the graph it is apparent that sin x cos x in the
