Q11,12,13 how to solve this type of ques:
11. f(x) = ax2 + bx + c where a 0. How many positive real roots does f(x) = 0 have if the maximum value of f(x) occurs at a root?
(1) 0 (2) 1 (3) 2 (4) Either (1) or (2)
(5) Either (2) or (3)
12. f(x) = ax2 + bx + c where a 0. How many positive real roots does f(x) = 0 have if f(x) = 0 has integral roots and the minimum-value-of f(x) is-2 at x = 0.5?
(1) 0 (2) 1 (3) 2 (4) Either (1) or (2)
(5) Either (2) or (3)
13. The equation ax2 + bx + c = 0, where a, b, c are real numbers, has one root greater than 2 and the other root less than zero. Which of the following is necessarily true?
(1) a(a + b + c) > 0
(2) a(a + b + c) < 0
(3) a+b+c > 0
(4) a+b+c <0
(1) 0 (2) 1 (3) 2 (4) Either (1) or (2)
(5) Either (2) or (3)
12. f(x) = ax2 + bx + c where a 0. How many positive real roots does f(x) = 0 have if f(x) = 0 has integral roots and the minimum-value-of f(x) is-2 at x = 0.5?
(1) 0 (2) 1 (3) 2 (4) Either (1) or (2)
(5) Either (2) or (3)
13. The equation ax2 + bx + c = 0, where a, b, c are real numbers, has one root greater than 2 and the other root less than zero. Which of the following is necessarily true?
(1) a(a + b + c) > 0
(2) a(a + b + c) < 0
(3) a+b+c > 0
(4) a+b+c <0