Assertion: the equation x² + 4 = 0 has no real roots. Reason: the discriminant of x² + 4 = 0 is −16. State whether the assertion and the reason are true and whether the reason explains the assertion.

Find the values of k for which x² + kx + 16 = 0 has equal roots.

Show that the equation 3x² − 2x + 1 = 0 has no real roots.

Find the nature of the roots of 4x² − 12x + 9 = 0 and solve the equation.

Find the value of k for which the equation kx² − 6x + 9 = 0 has equal roots.

Using the quadratic formula, solve 2x² + 5x − 3 = 0.

Solve x² − 2x − 8 = 0 and verify the roots by substitution.