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NEED HELP WITH THIS PLEASE. Just show me how please.

NEED HELP WITH THIS PLEASE. Just show me how please.-example-1

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Given:

The quadratic equation is:


-5x^2-3x-2=0

To find:

The discriminant of the given equation and the number of real solutions.

Solution:

If a quadratic equation is
ax^2+bx+c=0, then the value of discriminant is:


D=b^2-4ac

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,


-5x^2-3x-2=0

Here,
a=-5,b=-3,c=-2. So, the discriminant of the given equation is:


D=(-3)^2-4(-5)(-2)


D=9-40


D=-31

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.

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