6) Determine the nature of the roots for the quadratic equation
√3x + √2-2/3=0.
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Answer:
The given quadratic equation is
\sqrt{3}x^2+\sqrt{2}x-2\sqrt{3}=0
3
x
2
+
2
x−2
3
=0
A quadratic equation is ax^2+bx+c=0ax
2
+bx+c=0 .
If b^2-4ac < 0b
2
−4ac<0 , then the equation have two complex roots.
If b^2-4ac=0b
2
−4ac=0 , then the equation have equal real roots.
If b^2-4ac > 0b
2
−4ac>0 , then the equation have two distinct real roots.
In the given equation,
a=\sqrt{3},b=\sqrt{2},c=-2\sqrt{3}a=
3
,b=
2
,c=−2
3
b^2-4ac=(\sqrt{2})^2-4(\sqrt{3})(-2\sqrt{3})=2+24=26b
2
−4ac=(
2
)
2
−4(
3
)(−2
3
)=2+24=26
it is imaginary root
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