Algebra — practice questions, page 4
Browse practice questions
A two-digit number is 3 more than 4 times the sum of its digits. When 18 is added to it, the…The equations x² − 5x + 6 = 0 and x² − kx + 8 = 0 have a common root, and k is an integer. Find k.Simplify (a² − b²)(a² + ab + b²) ÷ [(a³ − b³)(a + b)].How many integers satisfy both 3x − 2 > 2x + 1 and 5x − 7 ≤ 3x + 13?When p(x) = x³ + ax + b is divided by (x − 1) and by (x + 1), the remainders are 5 and 3…Real numbers x and y satisfy 2x + 3y = 12 and xy = 6. Find 8x³ + 27y³.The sum of two numbers is 20 and the sum of their reciprocals is 5/24. Find the larger number.Positive numbers x and y have x² + y² = 25 and xy = 12. Find x³ + y³.For what value of a do 2x + 3y = 7 and (a − 1)x + (a + 2)y = 3a have infinitely many solutions?Positive integers x and y satisfy x² − y² = 45. How many ordered pairs (x, y) are there?For which values of m is x² + 2mx + (m + 6) positive for every real x?Find the sum of the real solutions of (x − 1)(x − 2)(x − 3)(x − 4) = 120.Find the remainder when x¹⁰⁰ is divided by x² − 1.For a > 0, simplify 1/(1 + a^(m−n) + a^(m−p)) + 1/(1 + a^(n−m) + a^(n−p)) + 1/(1 + a^(p−m) +…Taking x = 2 + 2^(1/3) + 2^(2/3), find x³ − 6x² + 6x.Let x = a(b − c), y = b(c − a) and z = c(a − b), with abc ≠ 0. Then (x/a)³ + (y/b)³ + (z/c)³ equalsFor 1 ≤ x ≤ 2, simplify √(x + 2√(x − 1)) + √(x − 2√(x − 1)).Let x = (√5 + 1)/(√5 − 1) and y = (√5 − 1)/(√5 + 1). Find (x² + y²)/(x² − y²).Two zeroes of x⁴ + 2x³ − 13x² − 14x + 24 are 1 and −2. Find the other two.A group of friends hired a bus for ₹4,800, sharing the cost equally. Four of them dropped out, so…Find the sum of all real x for which (x² − 5x + 5)^(x² − 9x + 20) = 1.p and q are the roots of x² − 2x + A = 0, and r and s are the roots of x² − 18x + B = 0. If p < q…If x² + y² + z² = 2(x − 2y + 3z) − 14 for real x, y, z, find x + 2y + 3z.The polynomial 2x³ + ax² + bx − 6 has (x − 2) as a factor and leaves remainder −15 on division by…
← Previous · Page 4 of 4