Given:
The quadratic equation is:
[tex]-5x^2-3x-2=0[/tex]
To find:
The discriminant of the given equation and the number of real solutions.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the value of discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then the quadratic equation has no real roots or two imaginary roots.
If D=0, then the quadratic equation has two equal real roots.
If D>0, then the quadratic equation has two distinct real roots.
We have,
[tex]-5x^2-3x-2=0[/tex]
Here, [tex]a=-5,b=-3,c=-2[/tex]. So, the discriminant of the given equation is:
[tex]D=(-3)^2-4(-5)(-2)[/tex]
[tex]D=9-40[/tex]
[tex]D=-31[/tex]
Since D<0, therefore the number of real solutions is 0.
Hence, the value of the discriminant is -31 and the number of real solutions is 0.
