find the zeros of 2root 3x^2 - 5x + root3
Answers
Answer:
Answer:
\text{The roots are }\frac{3}{2\sqrt3}, \frac{1}{\sqrt3}The roots are
2
3
3
,
3
1
Step-by-step explanation:
Given the equation
2\sqrt3 x^2-5x+\sqrt3=02
3
x
2
−5x+
3
=0
we have to find the roots of above equation using quadratic formula.
2\sqrt3 x^2-5x+\sqrt3=02
3
x
2
−5x+
3
=0
\text{Comparing above equation with }ax^2+bx+c=0\text{ , we get}Comparing above equation with ax
2
+bx+c=0 , we get
a=2\sqrt3, b=-5, c=\sqrt3a=2
3
,b=−5,c=
3
By quadratic formula
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=
2a
−b±
b
2
−4ac
x=\frac{-(-5)\pm \sqrt{(-5)^2-4(2\sqrt3)(\sqrt3)}}{2(2\sqrt3)}x=
2(2
3
)
−(−5)±
(−5)
2
−4(2
3
)(
3
)
x=\frac{5\pm\sqrt{25-24}}{4\sqrt3}x=
4
3
5±
25−24
x=\frac{5\pm 1}{4\sqrt3}x=
4
3
5±1
x=\frac{6}{4\sqrt3}, \frac{4}{4\sqrt3}x=
4
3
6
,
4
3
4
\text{Hence, the roots are }\frac{3}{2\sqrt3}, \frac{1}{\sqrt3}Hence, the roots are
2
3
3
,
3
1