Quant Boosters  Vikas Saini  Set 5

{x} = x – [x]
(a) 0
(b) 1
(c) 2
(d) 3

Hence 0.

Q28) When ‘2’ is added to each of the three roots of x^3  Ax^2 + Bx  C = 0, we get the roots of x^3 + Px^2 + Qx  18 = 0. If A, B, C, P and Q are all non zero real numbers then what is the value of (4A + 2B + C).

Let three roots of first equation are l, m, n respectively.
18 = (l+2)(m+2)(n+2)
18 = (lm+2l+2m+4)(n+2)
18 = lmn + 2lm + 2ln + 4l +2mn + 4m + 4n + 8.
10 = lmn + 2(lm+ln+mn) + 4(l+n+m)
10 = C+2B+4A.

Q29) If a, b and c are root of the equation 3x^3 + 42x + 93 = 0, then what is value of a^3 + b^3 + c^3 ?

Here coefficient of x^2 = 0.
means a+b+c = 0.
Then a^3 + b^3 + c^3 = 3abc = 93

Q30) ax^2 + bx + c = 0 is a quadratic equation with rational coefficients such that a + b + c = 0, then which of the following is necessarily true ?
(a) Both the roots of this equation are less than 1.
(b) One of the roots of the equation is c/a.
(c) Exactly one of the root is 1.
(d) b & c both.

let f(x) = ax^2 + bx + c
f(1) = a + b + c = 0.
Product of roots = c/a.
Hence option d.

@vikas_saini Thanks bro...very neat and nice explanation....keep doing this...perfect questions with perfect solutions...Thanks alot...:)

shouldn't we also consider the values less than 8? 1, 2, 3, 4, 5,6, 7?
as these would give negative results too.. please clarify.