Question Type 3: Finding how many roots the quadratic has Exercises

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

How many real roots does the quadratic equation $x^2 + 2x + 5 = 0$ have?

Find the value of $k$ such that the quadratic equation $kx^2 + 2x + 1 = 0$ has exactly one real root.

Determine the number of real solutions of $2x^2 - 8x + 6 = 0$.

Determine the range of values of $k$ for which the equation $kx^2 + 2x + 1 = 0$ has two distinct real roots.

How many real solutions does $4x^2 - 4x + 1 = 0$ have?

Find how many real roots the quadratic $3x^2 + 6x + 2 = 0$ has.

Determine the number of real roots of the quadratic equation $6x^2 - 5x + 105 = 0$.

Find the number of real roots of the quadratic $7x^2 + 14x + 7 = 0$.

Determine how many real roots the equation $10x^2 + 3x - 1 = 0$ has.

Determine the number of real solutions of $12x^2 - x + 3 = 0$.

How many real roots does the equation $x^2 + x + 1 = 0$ have?

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