Question

help needed asap 20 points if answered right

Answer 1

ANSWER

1. No real roots

2. $\frac{ 7\pm \: \sqrt{33} }{ - 4}$

3. The discriminant is negative.

EXPLANATION

1. The given equation is

$- 2 {x}^{2} - 9x - 5 = 0$

We have a=-2,b=-9 and c=-5.

The discriminant is given by:

$D= {b}^{2} - 4ac$

$D= {( - 9)}^{2} - 4( - 2)( - 5)$

This simplifies to:

$D= 36 - 40 = - 4$

Since the discriminant is less than zero, the quadratic equation has no real roots.

2. The given equation is:

$- 2 {x}^{2} - 7x - 2= 0$

We have a =-2, b=-7 and c=-2.

The roots of this equation are given by;

$x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

We plug in the values to get;

$x = \frac{ - - 7\pm \: \sqrt{ {( - 7)}^{2} - 4( - 2)( - 2) } }{2( - 2)}$

$x = \frac{ 7\pm \: \sqrt{33} }{ - 4}$

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.