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miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following​

roots of the quadratic 3
discriminant
nature of roots
sum of the roots
product of the roots​

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DᴀʀᴋPᴀʀᴀᴅᴏx

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

roots of the quadratic equation ~

  • [tex]2 \: \: \: \:a nd \: \: - 10[/tex]

discriminant ~

  • [tex]144[/tex]

nature of roots ~

  • [tex]real[/tex]

sum of the roots ~

  • [tex] - 8[/tex]

product of the roots ~

  • [tex] - 20[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve he given quadratic equation using quadratic formula ~

Let's consider the following values ~

  • b (Coefficient of x) = 8

  • a (Coefficient of x²) = 1

  • c (Constant term) = -20

According to quadratic formula, the roots are ~

  • [tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

where, ( b² - 4ac ) is known as it's discriminant ~

that is equal to ~

  • [tex](8) {}^{2} - (4 \times 1 \times - 20)[/tex]

  • [tex]64 - ( - 80)[/tex]

  • [tex]64 + 80[/tex]

  • [tex]144[/tex]

Hence, Discriminant = 144

And since discriminant is positive, then the roots of the quadratic polynomial are real .

Let's find the roots now ~

  • [tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac} }{2a} [/tex]

  • [tex] \dfrac{ - 8 \pm \sqrt{144} }{2 \times 1}[/tex]

  • [tex] \dfrac{ - 8 \pm12}{2} [/tex]

  • [tex] \dfrac{ 2( - 4 \pm6)}{2} [/tex]

  • [tex] - 4 \pm6[/tex]

So, the two roots are ~

  • [tex] - 4 + 6[/tex]

  • [tex]2[/tex]

and

  • [tex] - 4 - 6[/tex]

  • [tex] - 10[/tex]

Sum of roots ~

  • [tex] - 10 + 2[/tex]

  • [tex] -8[/tex]

product of roots ~

  • [tex] - 10 \times 2[/tex]

  • [tex] - 20[/tex]
Yes this can be correct just depends on if you do it

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