ANSWER
1. No real roots
2. [tex] \frac{ 7\pm \: \sqrt{33} }{ - 4}[/tex]
3. The discriminant is negative.
EXPLANATION
1. The given equation is
[tex] - 2 {x}^{2} - 9x - 5 = 0[/tex]
We have a=-2,b=-9 and c=-5.
The discriminant is given by:
[tex]D= {b}^{2} - 4ac[/tex]
[tex]D= {( - 9)}^{2} - 4( - 2)( - 5)[/tex]
This simplifies to:
[tex]D= 36 - 40 = - 4[/tex]
Since the discriminant is less than zero, the quadratic equation has no real roots.
2. The given equation is:
[tex] - 2 {x}^{2} - 7x - 2= 0[/tex]
We have a =-2, b=-7 and c=-2.
The roots of this equation are given by;
[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
We plug in the values to get;
[tex]x = \frac{ - - 7\pm \: \sqrt{ {( - 7)}^{2} - 4( - 2)( - 2) } }{2( - 2)} [/tex]
[tex]x = \frac{ 7\pm \: \sqrt{33} }{ - 4} [/tex]
3. The given graph is hanging downwards. This means that it doesn't have x-intercepts.
Therefore the roots are complex or imaginary.
This implies that, the discriminant of the corresponding equation is negative.
