Question

Show that the equation 2x^2-5x-4=0 has real and unreal roots

Answer 1

Answer:

Real and unequal roots.

Step-by-step explanation:

  Discriminant of ax^2 + bx + c - 0 is given by b^2 - 4ac, here,

a = 2, b = - 5, c = - 4.

So,

⇒ Discriminant = (-5)^2 - 4(-4*2)

         = 25 - 4( - 8 )

         = 25 + 32

         = 57

As 57 > 0, it means roots are real but unequal.

 Proved.

Answer 2

Given ,

The polynomial is 2x² - 5x - 4

We know that , the discriminant of quadratic equation is given by

$\star \: \: \sf \fbox{D = {(b)}^{2} - 4ac}$

Thus ,

$\sf \Rightarrow D= {( - 5)}^{2} - 4 \times 2 \times ( - 4) \\ \\ \sf \Rightarrow D = 25 + 32 \\ \\ \sf \Rightarrow D = 57 > 0$

$\therefore \sf \bold{ \underline{The \: quadratic \: eq \: has \: unequal \: and \: real \: roots </p><p>}}$