Algebra — practice questions, page 2
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The quadratic equation whose roots are 3 and −5 is:One root of the equation x² + px + 12 = 0 is 4. The other root is:The sum of a positive number and its reciprocal is 17/4. The larger of the two possible values of…A train covers 360 km at a uniform speed. If its speed had been 5 km/h more, the journey would…If the roots of x² + 2x + k = 0 are real and distinct, then:Which term of the arithmetic progression 21, 18, 15, ... is −81?The sum of the first 20 terms of an arithmetic progression with first term 5 and common difference…How many two-digit numbers are divisible by 7?In an arithmetic progression, 7 times the 7th term equals 11 times the 11th term. The 18th term is:Three numbers are in arithmetic progression. Their sum is 21 and their product is 231. The numbers…The sum of the first n terms of an arithmetic progression is Sₙ = 3n² + 5n. Its 10th term is:If x + y = 5, y + z = 7 and z + x = 8, then the product xyz equals:If x + y + z = 9, x + 2y + 3z = 20 and x + 3y + 6z = 35, then z equals:A purse holds ₹300 made up of ₹1, ₹2 and ₹5 coins. There are three times as many ₹1 coins as ₹5…The product of all the real roots of x⁴ − 13x² + 36 = 0 is:The largest root of 6x⁴ − 35x³ + 62x² − 35x + 6 = 0 is:The sum of all the real solutions of (x² + x)² − 8(x² + x) + 12 = 0 is:The roots of x/(x + 1) + (x + 1)/x = 5/2 are:If α and β are the roots of x² − 5x + 6 = 0, the quadratic equation whose roots are 2α and 2β is:The equation whose roots are the reciprocals of the roots of 3x² − 7x + 2 = 0 is:If α and β are the roots of x² − 4x + 1 = 0, then the equation whose roots are α + 3 and β + 3 is:The roots of x² + px + q = 0 are each 1 less than the roots of x² − 5x + 6 = 0. Then:The least value taken by the expression x² − 6x + 13 is:Two positive numbers add up to 24. The greatest possible value of their product is:The expression x² − 5x + 6 is negative exactly when:
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