Question

compute the value of the discriminant and give the number of real solutions of the quadratic equation. -2x²+3x+5=0

Answer 1

Given a quadratic equation in standard form

`y=ax^2+bx+c`

The discriminant D

`D=b^2-4ac`

tells the types of roots the equation has.

In this case, we have

`\begin{gathered} -2x^2+3x+5=0 \\ a=-2 \\ b=3 \\ c=5 \end{gathered}`

Then, the discriminant of this quadratic equation will be

`\begin{gathered} D=b^2-4ac \\ D=(3)^2-4(-2)(5) \\ D=9+40 \\ \mathbf{D=49} \end{gathered}`

Finally, the value of discriminat is 49 and as he discriminant is greater than zero then this quadratic equation has 2 different real solutions.