Algebra — practice questions, page 3
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Which statement about the expression x² + 4x + 7 is correct?x² + 2kx + 9 is positive for every real value of x when:If both (x − 2) and (x + 3) are factors of x³ + ax² + bx − 12, then:The polynomial x³ + ax² + bx + 10 is exactly divisible by (x − 2) and leaves the remainder 6 when…If (x + 2) is a factor of 2x³ + ax² + 11x + a + 3, then a equals:The HCF of the polynomials x⁴ − 16 and x² − 5x + 6 is:The HCF of two polynomials is (x + 3) and their LCM is (x − 2)(x + 3)(x + 4). If one of them is x²…For x ≠ 0, −1, −2 the sum 1/(x(x + 1)) + 1/((x + 1)(x + 2)) equals:If (3x + 5)/((x + 1)(x + 3)) = A/(x + 1) + B/(x + 3) for every admissible x, then B equals:For a ≠ 0 and a ≠ ±b, the value of (a² − b²)/(a² + ab) ÷ (a − b)/a is:The equation √(x + 7) = x − 5 is satisfied by:The sum of all values of x satisfying √(2x + 5) − √(x − 1) = 2 is:If y = √(6 + √(6 + √(6 + … ))) where the pattern continues without end, then y equals:The diagonal of a rectangle is 20 cm and its perimeter is 56 cm. The length of the rectangle is:The present ages of a mother and her daughter add up to 40 years. Five years ago the product of…Two taps together fill a tank in 12 hours. Working alone, the slower tap needs 10 hours more than…A boat travels 30 km upstream and 44 km downstream in a total of 10 hours. If the stream flows at…If a + b = 9 and ab = 14, with a > b, then a − b equals:If a − b = 4 and ab = 45, then a³ − b³ equals:If a + b = 7 and ab = 12, then 1/a² + 1/b² equals:In an arithmetic progression the sum of the first 7 terms is 49 and the sum of the first 17 terms…The 1st, 4th and 8th terms of an arithmetic progression with non-zero common difference are in…The sum of the first six terms of the geometric progression 3, 6, 12, ... is:If the 9th term of an arithmetic progression is zero, then its 29th term is:The solution of the inequality 3x − 7 < 5 + x, where x is a real number, is:
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