Algebra — practice questions, page 8
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QuestionIf x + y + z = 0, then (x + y)(y + z)(z + x) + xyz equals:QuestionIf x satisfies x² + x + 1 = 0, then the value of x¹⁰⁰ + x²⁰⁰ is:QuestionIf α is a root of x² − x − 1 = 0, then α³ expressed in the form pα + q is:QuestionIf α, β and γ are the zeros of x³ − 6x² + 7x − 2, then α² + β² + γ² equals:QuestionFor real x, the greatest value of 1/(x² − 4x + 7) is:QuestionTwo real numbers x and y satisfy x + y = 10. The least possible value of x² + y² is:QuestionFor x > 0, the least value of (x² + 4x + 9)/x is:QuestionIf f(x) = (x − 1)/(x + 1), then f(f(x)) equals:QuestionA function satisfies f(x + y) = f(x) · f(y) for all real x and y, and f(1) = 3. Then f(4) equals:QuestionThe numbers 2, x, 18 are in geometric progression and the numbers 2, y, 18 are in arithmetic…QuestionThe sum 1 + 3 + 9 + 27 + … of a geometric progression first exceeds 1000 when the number of terms…QuestionIn an arithmetic progression the sum of the first 10 terms is 155 and the sum of the first 20…QuestionHow many terms of the arithmetic progression 3, 8, 13, 18, … must be added to make a total of 570?QuestionThe 10th term counted from the last term of the arithmetic progression 4, 9, 14, …, 254 is:QuestionIf one zero of the polynomial x² − 7x + k is 3, then the other zero and the value of k are:QuestionA quadratic polynomial whose zeros are −3 and 5 is:QuestionFor what value of k does the pair of equations 2x + 3y = 7 and (k − 1)x + 6y = 14 have infinitely…QuestionThe equation 4x² − kx + 9 = 0 has two equal real roots. The positive value of k is:QuestionIf the nth term of an AP is given by aₙ = 5n − 3, then the sum of its first 10 terms is:QuestionUse a² − b² to evaluate (87)^2 - (13)^2/74.QuestionThe point (2, 3) lies on the line 2x + ky = 10. Find the value of k.QuestionThe cost of 2 pencils and 3 pens is ₹80, and the cost of 3 pencils and 2 pens is ₹70. The cost of…QuestionIf x + y + z = 0, then x^3 + y^3 + z^3 is equal to:QuestionIf the roots of the equation x² − 6x + k = 0 are equal, then the value of k isQuestionThe sum of the first 20 terms of the arithmetic progression 3, 7, 11, ... is
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