If the three points (0,1),(0.-1)and(x,0) are the vertices of an equilateral triangle,
Then find the values of x
Solution of Quadratic equations by factorisation

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√3,√2

√3, -√3

-√5,√3

√2,-√2

answer is B.

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Detailed Solution

Given, the three points(0,1),(0,-2) and (x,0) are the vertices of equilateral triangle.
ஃAB =BC=CA
Now, we will find the distance of AB, BC and CA using distance formula
d= √(x2-x1)2+(y2-y1)2 A=(0,1) ,B=(0,-2) ,C= (x,0)
AB=√(x2-x1)2+(y2-y1)2 =√(0-0)2+(-1-1)2 =√(-2)2 =√4
=2
BC= √(x3-x2)2+(y3-y2)2 =√(X-0)2+(0-(-1))2 =√X2+1
CA=√(x3-x1)2+(y3-y1)2 =√(X-0)2+(0-1)2 =√X2+1
AB=BC=CA
2=√X2+1
22=X2+1..taking square roots on both sides)
4= X2+1
X2=4-1
X2=3
X2=±√3
x= √3,-√3
Therefore,option 2 is the correct answer.
Type- CBSE
Subject- Mathematics
Chapter- Quadratic equations Topic- Solution of Quadratic equations by factorisation

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