Algebra — practice questions, page 3
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Form the quadratic whose roots are the squares of the roots of x² − 3x + 2 = 0.The sum of a number greater than 1 and its reciprocal is 10/3. Find the number.The product of two consecutive positive odd integers is 323. What is the larger one?A rectangular plot has an area of 528 m², and its length is 1 m more than twice its breadth. Find…A cyclist covers 72 km at a uniform speed. Had the speed been 6 km/h more, the ride would have…The squares of two consecutive natural numbers add up to 313. Find the larger number.For what positive k does x² − 2(k − 1)x + (k + 5) = 0 have equal roots?The roots of ax² + bx + c = 0 are in the ratio 2 : 3. Which relation holds?α and β are the roots of x² − 5x + 3 = 0. Which equation has roots α + 1/β and β + 1/α?x = 2 is a root of x² + ax − 10 = 0, and x² + ax + b = 0 has equal roots. Find b.Find the value of √(12 + √(12 + √(12 + …))) (continuing without end).The product of the digits of a two-digit number is 18. When 63 is subtracted from the number, its…A right triangle has an area of 30 cm² and a hypotenuse of 13 cm. Find the sum of its two shorter…What is the remainder when x³ + 2x² − 5x + 1 is divided by (x − 1)?Which value of x satisfies |x − 3| = 5 and is negative?How many integers x satisfy |2x − 5| ≤ 7?The zeroes of x³ − 6x² + 11x − 6 are α, β and γ. Find α² + β² + γ².For real x, what is the greatest value of 12 + 6x − x²?A polynomial p(x) leaves remainder 4 when divided by (x − 1) and remainder 10 when divided by (x −…The polynomial x³ + ax² + bx − 6 is divisible by both (x − 1) and (x − 2). Find a + b.If 2^a = 3^b = 6^c, which expression equals c?Find the sum of all solutions of 4^x − 3 · 2^(x + 1) + 8 = 0.Solve [√(x + 5) + √(x − 5)] ÷ [√(x + 5) − √(x − 5)] = 3.How many real numbers x satisfy x² − 5|x| + 6 = 0?The squares of three consecutive positive integers add up to 245. What is the sum of the three…
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