Respuesta :

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.

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