Using complete sentences, explain what the discriminant is and what it tells you about the solutions of a quadratic equation. Provide a unique example to back up your explanation.

Question

karatechopper · Answer

hello

across · Answer

Every 2nd order polynomial has three possible, general solutions: two unique roots, one repeated root and complex conjugate roots. The discriminant of a polynomial helps you determine which of those three cases you have.

paxpolaris · Answer

$$When\ ax^2+bx+c=0$$$$x={-b \pm \sqrt{b^2-4ac}\over2a}$$

across · Answer

For example, take$$x^2+2x-3.$$Its discriminant will be$$\sqrt{2^2-4(1)(-3)}=\sqrt{4+12}=\sqrt{16}=4.$$Since $4>0$, you know that this polynomial has two unique solutions.

paxpolaris · Answer

The discriminant is:$$b^2-4ac$$

across · Answer

For example, take$$x^2+4x+4.$$Its discriminant will be$$\sqrt{4^2-4(1)(4)}=\sqrt{16-16}=\sqrt{0}=0.$$Since your discriminant is $0$, you know that your polynomial will have a repeated root.

anonymous · Answer

thanks guys great answers

across · Answer

For example, take$$x^2+x+1.$$Its discriminant will be$$\sqrt{1^2-4(1)(1)}=\sqrt{1-4}=\sqrt{-3}.$$Since its (correct)* discriminant will be $-3$ and since that is less than zero, you know that your polynomial will have complex roots.

* I say correct because I took the square root of the discriminant in the above examples.

across · Answer

Forget the square root when computing discriminants.