Discuss the nature of roots of -x² + 3x + 1 = 0

Without sketching the graphs, find whether the graphs of the following functions will intersect the x-axis and if so in how many points. y = x² + 6x + 9

Solve |2x- 17| = 3 for x.

Solve 3|x - 2| + 7 = 19 for x.

Solve 3x - 5 ≤ x + 1 for x.

If a and b are the roots of the equation x² - px + q = 0, find the value of \(\frac{1}{a}+\frac{1}{b}\)

Simplify \(\sqrt{x^2-10x+25}\)

Rationalize the denominator of \(\frac{\sqrt{5}}{(\sqrt{6}+\sqrt{2})}\)

Find the logarithm of 1728 to the base 2\(\sqrt{3}\)

If the logarithm of 324 to base a is 4, then find a.