Answer:
D.
Step-by-step equation:
I don't know but i think this is the answer.
The roots of the equation are x = 0.5205 and x = -0.8538. These roots are real, rational and unequal, thus option (B) is the correct answer.
A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.
For the given situation,
The equation is 9x^2 + 3x – 4 = 0
The roots of the equation can be found by the formula,
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
here, a = 9, b = 3 and c = -4
Substitute the above values,
⇒ [tex]x=\frac{-3+\sqrt{3^{2}-4(9)(-4) } }{2(9)}[/tex] or [tex]x=\frac{-3-\sqrt{3^{2}-4(9)(-4) } }{2(9)}[/tex]
⇒ [tex]x=\frac{-3+\sqrt{9+144 } }{18}[/tex] or [tex]x=\frac{-3-\sqrt{9+144 } }{18}[/tex]
⇒ [tex]x=\frac{-3+\sqrt{153 } }{18}[/tex] or [tex]x=\frac{-3-\sqrt{153 } }{18}[/tex]
⇒ [tex]x=\frac{-3+12.36 }{18}[/tex] or [tex]x=\frac{-3-12.36 }{18}[/tex]
⇒ [tex]x=\frac{9.37}{18}[/tex] or [tex]x=\frac{-15.37}{18}[/tex]
⇒ [tex]x=0.5205[/tex] or [tex]x=-0.8538[/tex]
Hence we can conclude that the roots of the equation are x = 0.5205 and x = -0.8538. These roots are real, rational and unequal, thus option (B) is the correct answer.
Learn more about quadratic equation here
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