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JAVSON082006IN
Answered

What is the nature of the roots of the quadratic equation 5x²-4x-9=0?

A. Real,rational and equal
B. Real,rational and unequal
C. Real irrational and unequal
D. No real Roots

(Honest answer will get Brainliest)​

Sagot :

MIGGY6343IN

Answer:

No real Roots

hope it helps you

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RHOZETAIN

✏️ Nature of the Roots

[tex] {\Large{\overline{\underline{\sf{\hookrightarrow Answer:}}}}} [/tex]

  • The correct answer is letter B. The roots of the quadratic equation are real, rational, and unequal.

Solution:

Given the quadratic equation [tex] {\underline{\sf{5x^2 - 4x - 9 = 0}}} [/tex]

  • [tex] \sf a [/tex] = 5
  • [tex] \sf b [/tex] = -4
  • [tex] \sf c [/tex] = -9

Determine the nature of the roots using the discriminant of the quadratic formula.

[tex] {\large{\boxed{\sf{D = b^2 - 4ac}}}} [/tex]

  • [tex] \sf D = (-4)^2 - 4 (5) (-9) [/tex]
  • [tex] \sf D = 16 - 4 (-45) [/tex]
  • [tex] \sf D = 16 - (-180) [/tex]
  • [tex] \sf D = 16 + 180 [/tex]
  • [tex] {\sf \therefore D = {\boxed{\green{\sf{196}}}}} [/tex]

The discriminant is positive, so the roots are real and unequal. But since it is also a perfect square, since √196 = 14, we can therefore say that the roots are also rational.

So the correct answer is letter B.

[tex]{\: \:}[/tex]

[tex] {\huge{\overline{\sf{Hope\:It\:Helps}}}} [/tex]

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