Algebra — practice questions, page 5
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If α, β and γ are the zeros of x³ − 7x² + 14x − 8, then 1/α + 1/β + 1/γ equals:Two zeros of the cubic polynomial x³ − 4x² + x + 6 are 2 and 3. The third zero is:The zeros of x³ − 12x² + 39x − 28 are in arithmetic progression. The middle zero is:A man repays a loan of ₹3,250 by paying ₹20 in the first month and increasing the payment by ₹15…In a hall the first row has 20 seats and every following row has 2 seats more than the row in…Logs are stacked with 20 in the bottom row, 19 in the row above it, 18 in the next, and so on. If…A bacteria colony doubles every hour. If it has 500 bacteria at 9 a.m., how many will it have at 2…A machine bought for ₹6,25,000 loses 20% of its value every year. Its value at the end of 3 years…The sum of the infinite series 1 − 1/3 + 1/9 − 1/27 + … is:The arithmetic mean of two positive numbers is 10 and their geometric mean is 8. The numbers are:For two distinct positive numbers, which relation between the arithmetic mean (AM), geometric mean…If α and β are the roots of x² − 8x + 5 = 0, then α³ + β³ equals:If α and β are the roots of 3x² + 5x − 2 = 0, then α/β + β/α equals:In an arithmetic progression the 4th term is 11 and the 12th term is 35. Its 20th term is:If α and β are the roots of 2x² − 7x + 3 = 0, then (α − β)² equals:The sum of the squares of the roots of x² − (p − 2)x − (p + 1) = 0 is smallest when p equals:A quadratic equation with rational coefficients has 2 + √5 as one root. The equation is:If α and β are the roots of x² − 3x + 2 = 0, then the equation whose roots are α² and β² is:The quadratic equation with integer coefficients whose roots are 1/2 and −2/3 is:The equation (k + 4)x² + (k + 1)x + 1 = 0 has equal roots for which values of k?The equation 2x² + 3x + k = 0 has no real root when:One root of x² − (k + 3)x + 8 = 0 is twice the other. The positive value of k is:The equations x² − 7x + 12 = 0 and x² − 9x + 20 = 0 have exactly one root in common. That root is:The equations x² + 2x + k = 0 and x² + kx + 2 = 0, with k ≠ 2, share a common root. That root is:One factor of x³ + x² − 4x − 4 is (x + 1). The remaining two factors are:
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