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What is the nature of roots for the equation a^2 - 2a -15= 0?

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UK2019go

✏️QUADRATIC

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Problem: What is the nature of roots for the quadratic equation a² - 2a - 15 = 0?

Solution: We can use the Formula to find the discriminant then classify the nature of roots.

[tex]\begin{aligned}&\bold{\color{lightblue}Formula:} \\&\boxed{D = b^2 - 4ac} \end{aligned}[/tex]

  • [tex]D = (\text - 2)^{2} - 4(1)( \text - 15)[/tex]

  • [tex]D = 4 - 4(1)( \text - 15)[/tex]

  • [tex]D = 4 - 4(\text - 15)[/tex]

  • [tex]D = 4 - (\text - 60)[/tex]

  • [tex]D = 4 + 60[/tex]

  • [tex]D = 64[/tex]

- The discriminant is positive, but it is a perfect square, therefore our nature of roots of the quadratic equation is:

  • Real, Rational and Unequal

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