Question

what does it mean "compute the discriminant" of the quadratic equation 2x2 – 3x – 5 = 0
I can calculate the equation but don't understand the discriminant or how to describe the number of solutions and types of solutions?

Answer 1

the discriminant is defined as \(b^2-4ac\) for a standard quadratic equation of the form \(ax^2+bx+c=0\).
if the discriminant is negative, then you know you have 2 complex roots
if the discriminant is positive, then you know you have 2 real roots
if the discriminant is zero, then you know you have 2 equal real roots

Answer 2

ok, i still don't understand what it means...
when i figure it out i get x=(-3±49)/4

Answer 3

what you have listed are the roots of the equation.
the discriminant is just the value of \(b^2-4ac\)

Answer 4

in your case, it would be:\[(−3)^2−4∗2∗(−5)=9+40=49\]so in your case, you can tell that you will have 2 real roots.