Question Type 7: Determining the number of real roots for a given real quadratic Exercises

Determine the number of real roots of the quadratic equation $x^2 - 4x + 4 = 0$.

Determine the number of real roots of the quadratic $x^2 + x + 1 = 0$.

Show that the quadratic $4x^2 - 6x + 5 = 0$ has no real solutions.

Determine the number of real solutions to $2x^2 - 5x + 2 = 0$.

Determine the number of real roots of $x^2 + 4x + 3 = 0$.

Determine the number of real roots of $5x^2 - 20x + 15 = 0$.

Find all real values of $k$ for which the equation $x^2 - 2x + k = 0$ has real roots.

For what values of $k$ does $x^2 - 6x + k = 0$ have no real roots?

Find the range of $k$ for which $4x^2 - 6x + k = 0$ has two distinct real roots.

Determine the value(s) of $k$ such that the quadratic $3x^2 + kx + 1 = 0$ has exactly one real root.

For $k>0$, determine the number of real roots of $kx^2 + 4x + 1 = 0$ in terms of $k$.

Determine all real $k$ such that $x^2 + 2(k-1)x + k = 0$ has real roots.