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Sagot :
Answer: Two real solutions
1. Identify the coefficients , and of the quadratic equation.
a=1, b= -15, c=12
2. Evaluate the discriminant by substituting , and into the expression.
(-15)^2 - 4 • 1 • 12
3. Simplify the expression
177 - The discriminant is greater than 0, so the quadratic equation has two real solutions.
1. Identify the coefficients , and of the quadratic equation.
a=1, b= -15, c=12
2. Evaluate the discriminant by substituting , and into the expression.
(-15)^2 - 4 • 1 • 12
3. Simplify the expression
177 - The discriminant is greater than 0, so the quadratic equation has two real solutions.
Answer:
2 real solutions.
Step-by-step explanation:
Discriminant
[tex]\boxed{b^2-4ac}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}.[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}.[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}.[/tex]
Given equation:
[tex]x^2-15x+12=0[/tex]
Therefore:
- a = 1
- b = -15
- c = 12
Substitute these values into the discriminant formula:
[tex]\begin{aligned}\implies b^2-4ac&=(-15)^2-4(1)(12)\\&=225-48\\&=177\end{aligned}[/tex]
Therefore, as b² - 4ac > 0 there are two real solutions.
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