LOCATION OF ROOTS : Let f(x) = ax2 + bx + c, where a > 0 & a, b, c e R. If there be any two real numbers 'a' & 'b' such that f(a) & f(b) are of opposite signs, then f(x) = 0 must have atleast one real root between 'a' and 'b'.Įvery equation f(x) = 0 of degree odd has atleast one real root of a sign opposite to that of its last term. If the coefficients in the equation are all rational & a + ^P is one of its roots, then a - ^P is also a root where a, p € Q & p is not a perfect square. imaginary roots occur in conjugate pairs. If the coefficients of the equation f(x) = 0 are all real and a + ip is its root, then a - ip is also a root. Sin 9 + c o s 9 = 1 sec2 9 - tan2 9 = 1 cosec2 9 - cot2 9 = 1ĬONCEPTS -l 1) has exactly n roots & if the equation has more than n roots, it is an identity.
BANSAL CLASSES MATHEMATICS TARGET IIT JEE 2007 XI (P, Q, R, S)ĬOMPOUND ANGLES Trigonometry Phase - / »iĬONTENTS KEY-CONCEPTS EXERCISE-I EXERCISE -II EXERCISE-III ANSWER KEY
