The coefficients of x in the quadratic equation x2 + bx + c = 0 was taken as 17 in place of 13, its roots were found to be – 2 and -15. The correct roots of the original equation are
1) – 10, – 3 2) – 9, – 4 3) – 8, – 5 4) – 7, – 6... View Article
Latest Posts
The solution set of the equation pqx2 – (p + q)2 x + (p + q)2 = 0 is
1) {p / q, q / p} 2) {pq, p / q} 3) {q / p, pq} 4) {[p +... View Article
Let a, b be the solutions of x2 + px + 1 = 0 and c, d be the solutions of x2 + qx + 1 = 0. If (a – c) (b – c) and (a + d) (b + d) are the solutions of x2 + αx + β = 0, then β equals
1) P + q 2) p – q 3) p2 + q2 4) q2 – p2 Solution: (4) q2 –... View Article
The roots of the equation x4 – 2x3 + x = 380 are
1) 5, – 4, [1 ± 5 √- 3] / 2 2) – 5, 4, [- 1 ± 5 √-... View Article
If sin A, sin B and cos A are in GP, then the roots of x2 + 2x cot B + 1 = 0 are always
1) real 2) imaginary 3) greater than 1 4) equal Solution: (1) real sin A, sin B, cos A are... View Article
If the cube roots of unity are 1, ω and ω2 then the roots of the equation (x – 1)3 + 8 = 0, are
1) – 1, 1 + 2ω , 1 + 2ω2 2) – 1, 1 – 2ω, 1 – 2ω2 3)... View Article
The roots of the equation x3 – 3x2 – 6x + 8 = 0 are in arithmetic progression, then the roots of the equation are
1) 3, 4 , 5 2) 4, 7, 10 3) – 2, 1, 4 4) 1, 4, 7 Solution: (3)... View Article
The difference between two roots of the equation x3 – 13x2 + 15x + 189 = 0 is 2. Then, the roots of the equation are
1) -3, 7, 9 2) -3, – 7, – 9 3) -3, – 5, 7 4) -3, -7, 9 Solution:... View Article
If f (x) = 2x3 + mx2 – 13x + n and 2, 3 are the roots of the equation f (x) = 0, then the values of m and n are
1) -5 , – 30 2) -5 , 30 3) 5 , 30 4) None of these Solution: (2) -5... View Article
The roots of the equation (q – r) x2 + (r – p) x + (p – q) = 0 are
1) [r – p] / [q – r], 1 2) [p – q] / [q – r], 1 3) [p... View Article
If a, b and c are the sides of ∆ABC such that a ≠ b ≠ c and x2 – 2(a + b + c ) x + 3λ (ab + bc + ca ) = 0 has real roots, then
1) λ < (4 / 3) 2) λ > (5 / 3) 3) λ ∈ (4 / 3, 5 /... View Article
If x2/3 – 7x1/3 + 10 = 0, then the value of x is
1) 125 2) 8 3) ∅ 4) 125, 8 Solution: (4) 125, 8 x2/3 – 7x1/3 + 10 = 0... View Article
The solution of the equation 2x3 – x2 – 22x – 24 = 0 when two of the roots are in the ratio 3 : 4, is
1) 3, 4, (1 / 2) 2) – (3 / 2) , – 2, 4 3) – 1 / 2,... View Article
The maximum number of real roots of the equation x2n – 1 = 0 is
1) 2 2) 3 3) n 4) 2n Solution: (1) 2 x2n – 1 = 0 x2n = 1 There... View Article
If 1, 2, 3 and 4 are the roots of the equation x4 + ax3 + bx2 + cx + d = 0, then a + 2b + c is equal to
1) – 25 2) 0 3) 10 4) 24 Solution: (3) 10 1 + 2 + 3 + 4 =... View Article
The number of real solutions of the equation (9 / 3) = – 3 + x – x2 is
1) 0 2) 1 3) 2 4) None of these Solution: (1) 0 Let f (x) = – 3 +... View Article
Both the roots of the equation (x – a) ( x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 are always
1) positive 2) negative 3) real 4) imaginary Solution: (3) real (x – a) ( x – b) + (x... View Article
If ecos x – e-cos x = 4, then the value of cos x is
1) log(2 + √5) 2) – log(2 + √5) 3) log( – 2 + √5) 4) None of the above... View Article
If (1 – p) is a root of quadratic equation x2 + px + (1 – p) = 0, then its roots are
1) 0, 1 2) – 1, 1 3) 0, – 1 4) – 1, 2 Solution: (3) 0, – 1... View Article
The number of real roots of the equation (x + (1 / x))3 + x + (1 / x) = 0 is
1) 0 2) 2 3) 4 4) 6 Solution: (1) 0 (x + 1 / x)3 + (x + 1... View Article
