Related InterviewSolutions

• If α,β are roots of the equation (x–a)(x–b)+c = 0 (c ≠ 0), then then roots of the equation (x – c – α)(x – c – β) = c are(a)  a and b + c(b)  a + c and b(c) a + c and b + c(d)  None of these 
• If a ∈ Z and the equation (x – a)(x – 10) +1 = 0 has integral roots, then the values of a are(a)  10, 8(b)  12, 10(c)  12, 8(d)  None of these 
• The polynomial equation (ax2+bx+c)(ax2–dx–c) = 0 , ac ≠ 0 has (a) four real roots(b) atleast two real roots(c) atmost two real roots(d) No real roots 
• If a, b, c ∈ R , and the equation ax2 + bx + c = 0 has no real roots, then (a)  (a + b + c) > 0(b)   a(a + b + c) > 0(c)   b (a + b + c) > 0(d)   c(a + b + c) < 0 
• The values of p for which 6 lies between the roots of the equation x2 + 2(p – 3)x + 9 = 0 is(a) (-∞, -3/4)(b)  (-∞, -3/4)(c)  (-∞, 1)(d) none of these
• The values of m(m ∈ R), for which both roots of the equation x2–6mx + 9m2 – 2m + 2 = 0 exceed 3 is(a)  (-∞, 1)(b)  (-∞, 1)(c)  (1, ∞)(d)  none of these
• The values of m for which both roots of the equation x2 – mx + 1 = 0 are less than unity is(a) (-∞, -2)(b) (-∞, -2)(c) (-2, -∞)(d)  none of these
• If α ,β are roots of the equation x2 – 2x +  3 = 0 Then the equation whose roots are  α3–3 α2 + 5α – 2 and  β3 – β2 + β + 5 is(a)  x2 + 3x + 2 = 0(b)  x2– 3x – 2 = 0(c)  x2 – 3x + 2 = 0(d)  None
• The all possible values of a for which one root of the equation (a – 5)x2 – 2ax + a – 4 = 0 is smaller than 1 and the other greater than 2 is (a)  [5, 24) (b)  (5, 24] (c)  (5, 24) (d)   none of these