NiceFriendLikeYou
Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

characterize the roots of the following quadratic equation using the discriminant
1) x²+4x+3=0
2)x²-5x+4=0​

Sagot :

semsee45

Answer:

1)  Two real roots

2)  Two real roots

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots\\when $b^2-4ac=0 \implies$ one real root\\when $b^2-4ac < 0 \implies$ no real roots\\\end{minipage}}[/tex]

Question 1

[tex]\textsf{Given equation}: \quad x^2+4x+3=0[/tex]

[tex]\textsf{Therefore}: \quad a = 1, \:\:b = 4, \:\:c = 3[/tex]

Substitute these values into the discriminant formula:

[tex]\begin{aligned} \implies b^2-4ac & = 4^2-4(1)(3)\\ & =16-12\\ & =4\end{aligned}[/tex]

[tex]\textsf{As }\:b^2-4ac =4 > 0 \implies \textsf{two real roots}[/tex]

Question 2

[tex]\textsf{Given equation}: \quad x^2-5x+4=0[/tex]

[tex]\textsf{Therefore}: \quad a = 1, \:\:b = -5, \:\:c = 4[/tex]

Substitute these values into the discriminant formula:

[tex]\begin{aligned} \implies b^2-4ac & = (-5)^2-4(1)(4)\\ & =25-16\\ & =9\end{aligned}[/tex]

[tex]\textsf{As }\:b^2-4ac =9 > 0 \implies \textsf{two real roots}[/tex]

Learn more about the discriminant here:

https://brainly.com/question/27869538

https://brainly.com/question/27796651

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.