Class 10 Mathematics: Advanced Quadratic Equations

If the roots of the quadratic equation (b - c)x² + (c - a)x + (a - b) = 0 are equal, then which of the following is true?

For what value of k, the roots of the quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 are real and equal?

If one root of the equation x² + px + q = 0 is the square of the other, then which of the following relations is correct?

If sinθ and cosθ are the roots of the equation ax² + bx + c = 0, then which among the following is true?

A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, then the number of days B alone would take to finish the work is:

If the roots of the equation x² + 2cx + ab = 0 are real and unequal, then the roots of x² - 2(a + b)x + a² + b² + 2c² = 0 are __________.

If the equation x² – 8x + k = 0 has a repeated root, then the value of k is __________.

The value of k for which the quadratic equation kx(x - 2) + 6 = 0 has two equal roots is __________.

Solve for x: (1 / (a + b + x)) = (1/a) + (1/b) + (1/x), where a+b ≠ 0.

Find the values of 'p' for which the quadratic equation (2p + 1)x² - (7p + 2)x + (7p - 3) = 0 has equal roots.