Question:

Consider the quadratic equation cx² - cx + c - 40 = 0, c ≠ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is?

Letf(x)=(c𕒹)c2𕒶cx+c𕒸∴f(0)f(2)<0 (1) f(2)f(3)<0.. (2)from(1) (2)(c𕒸)(c𕒶4)<0 (c𕒶4)(4c󔼹)<0⇒494<c<24∴s=13,14,15,.23Number of elements in set S=11.