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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Let's find the discriminant (D) of the given polynomial ~

Let's compare the given quadratic expression with general expression ~

[tex] \boxed{ \boxed{ \sf {ax}^{2} +b x + c }}[/tex]

we get ;

  • [tex] \sf \: a = 2[/tex]
  • [tex] \sf \: b = 5[/tex]
  • [tex] \sf \: c = - 8[/tex]

Now, use the following formula :

[tex]\qquad \sf \dashrightarrow \: D = b² - 4ac[/tex]

[tex]\qquad \sf \dashrightarrow \: D = (5) {}^{2} - (4 \times 2 \times ( - 8))[/tex]

[tex]\qquad \sf \dashrightarrow \: D = 25 - ( - 64)[/tex]

[tex]\qquad \sf \dashrightarrow \: D = 25 + 64[/tex]

[tex]\qquad \sf \dashrightarrow \: D = 89[/tex]

Therefore, discriminant of the given quadratic expression is 89

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