Quadratic Discriminant Practice Problems

Here you will find a concise collection of quadratic discriminant practice problems. Visit this page directly at hunkim.com/discriminant

$D=b^2-4ac$ . Where does this formula come from?
Find the discriminant of the following quadratic: $y=x^2+2x-8$ .
What is the meaning of:
1. $D>0$
2. $D=0$
3. $D<0$
4. $D\leq0$
Show that the quadratic equation $x^2+(2k+3)x+k^2+3k+1=0$ has two distinct real roots in $x$ , for all values of the constant $k$ .
Find the exact values of $k$ for which the quadratic equation $kx^2-(k+1)x+2=0$ has a repeated root.
Find the range of values of the constant $k$ so that the graph of the curve with equation $y=x^2+5k+k$ does not cross the $x-axis$ .
Find the y-intercept of a line with a slope of $-3$ that is tangent (means just barely touching) the curve $y=2x^2-4x-3$ .
Find the range of values of the parameter $c$ such that $2x^2-3x+(2x+1)\geq0$ for all $x$ .
The positive difference between the zeros of the quadratic expression $x^2+kx+2$ is $\sqrt{50}$ . Find the possible values of $k$ .
Find the exact values of $m$ for which the line $y=mx+2$ and the curve with equation $y=2x^2+x+4$ have only one point of intersection.
Find the discriminant: $2x^2+4x-5$
Show that the quadratic equation $x^2+(2k+3)x+k^2+3x+1=0$ has two distinct real roots in $x$ for all values of the constant $k$ .
Find the discriminant: $2x^2+4x-5$
Show that the quadratic equation $x^2+(2k+3)x+k^2+3x+1=0$ has two distinct real roots in $x$ for all values of the constant $k$ .