Daily Exam 2 – Algebra

Determine the value of k so that the sum and product of the roots are equal from the given equation 7x² + (2k – 1)x – 3k + 2 = 0.

Find the constant k in x² – 4x + 3k = 0 if one root exceed the other by 2.

The equation whose roots are the reciprocal of the roots of 2x² – 3x – 5 = 0 is:

Find the constant k in 2x² – 3k²x = 8 – 6kx given that one root is negative of the other.

Find the value of k in the quadratic equation 3x² – kx + x -7k = 0 if 3 is one of the roots.

Find the middle term of the expansion of (x² + 1)¹⁶.

What is the sum of the coefficient of the expansion of (2x – 1)²⁰.

Find the value of x if the 8th term of the expansion of (x³ + 1)¹² is equal to 25952256.

The 5th term of the expansion of (x² + 1/x)ⁿ is 210x⁸. Find the value of n.

Find the term involving x⁸ in the expansion of (x² + 1/x)¹⁶.

Find the coefficient of (x + y)¹⁰ containing the term x⁷y³.

Find the 6th term of the expansion of (1/2a – 3)¹⁶.

Reduce to simple fraction: [x/(x + y) + 1] / [1 – 3x/(x – y)]

Reduce to lowest terms: (a² – b²) / (a² – 4ab + 3b²)

Factor the expression 3x³ – 3x² – 18x