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Use the discriminant to describe the solutions as one real, two real, or two imaginary solutions.

x^2 - 15x + 12 = 0

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.
semsee45

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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