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:
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