If α, β and γ are the roots of the equation x3 – 3x2 + x + 5 = 0, then y = ∑α2 + αβγ satisfies the equation
1) y3 + y + 2 = 0 2) y3 – y2 – y – 2 = 0 3) y3... View Article
Latest Posts
Root 4,……. are the roots of the equation
1) x2 – 4 = 0 2) x2 – 4x + 6 = 0 3) x2 – 5x + 4... View Article
Let α and β are the roots of equation 2x2 – (p + 1) x + (p – 1) = 0. If α – β = αβ, then what is the value of p ?
1) 1 2) 2 3) 3 4) – 2 Solution: (2) 2 Since α + β = [p + 1]... View Article
If α, β and γ are the roots of x3 + 2x2 – 3x – 1 = 0, then α-2 + β-2 + γ-2 is equal to
1) 12 2) 13 3) 14 4) 15 Solution: (2) 13 It is given that ∑α = – 2 ∑αβ... View Article
If α and β are the roots of the equation x2 – 6x + a = 0 and satisfy the relation 3α + 2β = 16, then the value of a is
1) – 8 2) 8 3) – 16 4) 9 5) None of these Solution: (2) 8 Since α +... View Article
If 3p2 = 5p + 2 and 3q2 = 5q + 2, where p ≠ q, then the equation, whose roots are 3p – 2q and 3q – 2p, is
1) 3x2 – 5x – 100 = 0 2) 5x2 + 3x + 100 = 0 3) 3x2 – 5x... View Article
The condition that x3 – px2 + qx – r = 0 may have two of its roots equal in magnitude but of opposite sign, is
1) r = pq 2) r = 2p3 + pq 3) r = p2q 4) None of these Solution: (1)... View Article
In ∆ PQR, ∠R = π/2. If tan (P/2) and tan (Q/2) are the roots of ax2 + bx + c = 0 , a ≠ 0, then
1) b = a + c 2) b = c 3) c = a + b 4) a = B... View Article
Let α and β be the roots of the equation ax2 + bx + c = 0 and ∆ = b2 – 4ac . If α + β, α2 + β2 and α3 + β3 are in GP, then
1) ∆ ≠ 0 2) b/∆ = 0 3) c∆ = 0 4) bc ≠ 0 Solution: (3) c∆ =... View Article
If sin θ + cos θ = h, then the quadratic equation having sin θ and cos θ as its roots, is
1) x2 – hx + (h2 – 1) = 0 2) 2x2 – 2hx + (h2 – 1) = 0... View Article
If a , c ≠ 0 and α, β are the roots of the equation ax2 + bx + c = 0, then the quadratic equation with 1/α and 1/β as its roots, is
1) x2/a + x/b + 1/c = 0 2) cx2 + bx + a = 0 3) bx2 + cx... View Article
If α, β and γ are the roots of x3 + bx + c = 0, then α2β + αβ2 + β2γ + βγ2 + γ2α + γα2
1) c 2) – c 3) – 3c 4) 3c Solution: (4) 3c Since α + β + γ =... View Article
The quadratic equation, whose roots are sin2 180 and cos2 360, is
1) 16x2 – 12x + 1 = 0 2) 16x2 + 12x + 1 = 0 3) 16x2 – 12x... View Article
If α ≠ β and a2 = 5α – 3, β2 = 5β – 3, then the equation having α/β and β/α as its roots is
1) 3x2 + 19x + 3 = 0 2) 3x2 – 19x + 3 = 0 3) 3x2 – 19x... View Article
If ω and ω2 are the two imaginary cube roots of unity, then the equation, whose roots are aω317 and aω382, is
1) x2 + a2x + a2 = 0 2) x2 + a2x + a = 0 3) x2 – ax... View Article
If α and β are the roots of the equation 6x2 – 5x + 1 = 0, then the value of tan-1 α + tan-1 β is
1) 0 2) π / 4 3) 1 4) /2 Solution: (2) π / 4 6x2 – 5x + 1... View Article
If α and β are the roots of the equation x2 – 7x + 1 = 0, then the value of 1 / (α – 7)2 + 1 / (β – 7)2 is
1) 45 2) 47 3) 49 4) 50 5) 51 Solution: (2) 47 x2 – 7x + 1 = 0... View Article
If a, b, and c are in geometric progression and the roots of the equation ax2 + 2bx + c = 0 are α , β and those of cx2 + 2bx + a = 0 are γ, δ, then
1) α ≠ β ≠ γ ≠ δ 2) α ≠ β and γ ≠ δ 3) aα = aβ... View Article
If α1, α2, and α3 are the roots of the equation x4 + (2 √3)x2 + 2 + √3 = 0, then the value of (1 – α1) (1 – α2) (1 – α3) (i – 1 – α4) is
1) 1 2) 4 3) 2 + √3 4) 5 5) 0 Solution: (4) 5 α1, α2, and α3 are... View Article
If α, β and γ are the roots of the equation 2x3 – 3x2 + 6x+ 1 = 0, the α2 + β2 + γ2 is equal to
1) – (15 / 4) 2) 15/4 3) 9/4 4) 4 Solution: (1) – (15 / 4) It is given... View Article
