Latest Posts

If x² + px + q = 0 has the roots α and β, then the value of (α – β)² is

1) p2 – 4q 2) (p2 – 4q)2 3) p2 + 4q 4) (p2 + 4q)2 Solution: (1) p2 –... View Article

If one root of the equation x² + px + q = 0 is 2 + √3, then the values of p and q are respectively

1) – 4, 1 2) 4, -1 3) 2,√3 4) – 2, -√3 Solution: (1) – 4, 1 If 2... View Article

If α and β are the roots of the equation ax² + bx + c = 0 (c ≠ 0), then the equation, whose roots are 1 / [aα + b] and 1 / [aβ + b], is

1) acx2 – bx + 1 = 0 2) x2 – acx + bc + 1 = 0 3) acx2... View Article

If α and β are the roots of the equation x² – x + 1 = 0, then α²⁰⁰⁹ + β²⁰⁰⁹ is equal to

1) – 2 2) – 1 3) 1 4) 2 Solution: (3) 1 x2 – x + 1 = 0... View Article

Let p and q be real numbers such that p ≠ 0, p³ ≠ q and p³ ≠ – q. If α and β are non – zero complex numbers satisfying α + β = – p and α³ + β³ = q, then a quadratic equation having α / β and α / β as its roots is

1) (p3 + q)x2 – (p3 + 2q)x + (p3 + q ) = 0 2) (p3 + q)x2 –... View Article

If α, β and γ are the roots of x³ – 2x + 1 = 0 then the value of ∑ [1] / [α + β – γ] is

1) -1 / 2 2) -1 3) 0 4) 1/2 Solution: (2) -1 x3 – x – x + 1... View Article

If α and β are the roots of the equation x² – 2x + 4 = 0, then the value of αⁿ + βⁿ will be

1) i2n+1 sin (nπ/3 ) 2) 2n+1 cos (nπ/3 ) 3) i 2n-1 sin (nπ/3 ) 4) 2n-1 cos (nπ/3... View Article

If the product of the roots of the equation x² – 2 √2kx + 2e^2logk – 1 = 0 is 31, then the roots of the equation are real for k, is equal to

1) – 4 2) 1 3) 4 4) 0 Solution: (3) 4 Product = 31 2e2logk – 1 = 31... View Article

If (α + √β ) and (α -√β ) are the roots of the equation where x² + px + q = 0, where α, β p and q are real, then the roots of the equation (p² – 4q) (p²x² + 4px) – 16q = 0 are

1) [(1 / ɑ) + (1 / √β)] and [(1 / ɑ) – (1 / √β)] 2) [(1 / √ɑ)... View Article

If α , β and γ are the roots of the equation x³ + 4x + 2 = 0, then α³ + β³ + γ³ is equal to

1) 2 2) 6 3) – 2 4) – 6 Solution: (4) – 6 x3 + 4x + 2 =... View Article

If (x² + px + 1) is a factor of (ax³ + bx + c), then

1) a2 + c2 = – ab 2) a2 – c2 = – ab 3) a2 – c2 = ab... View Article

If the roots of the equation ax² + bx + c = 0 are of the form [k + 1] / k and [k + 2] / [k + 1] then (a + b + c)² =

1) b2 – 4ac 2) b2 – 2 ac 3) 2b2 – ac 4) ∑a2 Solution: (1) b2 – 4ac... View Article

If the arithmetic mean of the roots of a quadratic equation is 8 and the geometric mean is 5, then the equation is

1) x2 – 16 x – 25 = 0 2) x2 + 16 x – 25 = 0 3) x2... View Article

If the roots of ax² + bx + c = 0 are sin α and cos β for some α, then which one of the following is correct?

1) a2 + b2 = 2ac 2) b2 – c2 = 2ab 3) b2 – a2 = 2ac 4) b2... View Article

If α and β are the roots of the equation ax² + bx + c = 0 and S_n = αⁿ + βⁿ and a S_n+1 + b S_n + c S_n-1 is equal to

1) 0 2) abc 3) a + b + c 4) None of these Solution: (1) 0 α + β... View Article

Let f (x) = 2x² + 5x + 1. If we write f (x ) as f (x) = [a (x + 1) (x – 2) + b (x – 2) (x – 1) + c(x – 1)(x + 1)] for real numbers a,b and c, then

1) there are infinite numbers of choices for a, b and c 2) only one choice for a but infinite... View Article

If α, β are the roots of ax² + bx + c = 0 (a ≠ 0) and α + h, β + h are the roots of px² + qx + r = 0 (p ≠ 0), then the ratio of the squares of their discriminants is

1) a2 : p2 2) a : p2 3) a2 : p 4) a : 2p Solution: (1) a2 :... View Article

If a, b and c are positive numbers in a GP, then the roots of the quadratic equation (log_e a) x² – 2 (log_e b) x + (log_e c) = 0 are

1) – 1 and [loge c] / [loge a] 2) 1 and – [loge c] / [loge a] 3) 1... View Article

If the roots of the equation x² + 2bx + c = 0 are α and β, then b² – c is equal to

1) (α – β)2 / 4 2) (α + β)2 – αβ 3) (α + β)2 + αβ 4) [(α... View Article

If α and β are the roots of the equation x² + 3x – 4 = 0, then 1/α + 1/β is equal to

1) -3/4 2) 3/4 3) -4/3 4) 4/3 5) 3/2 Solution: (2) 3 / 4 α + β = –... View Article

«
1
…
3,005
3,006
3,007
3,008
3,009
…
5,472
»