Question

x2 - (root3 + 1)x +root 3 = 0
solve using quadratic formula.​

Answer 1

X-(√3+1)X+√3=0

=X2-√3x - 1 × X + √3=0

[√3×1=√3 = √3 = -√3 × -1 = (√3+1)=-√3-1]

=X(X-√3)-1 (X-√3)=0

=(X-√3)(X-1)=0

=X-√3=0 or X-1=0

=X=√3 or X=1

X-1 and X=√3 are the two roots of the given

quadratic equation

Answer 2

Explanation:

The coefficient of x² is 'a', the coefficient of x is 'b' and the constant term is 'c'.

So, a= 1 ( since there is no coefficient given)

b= - (✓3 +1)

c=✓3

Discriminant= b²-4ac

Substitute the values of a, b and c

D= -(✓3+1)²-4* 1* ✓3

= (✓3)²+ 2* ✓3* 1+ 1²- 4✓3

= (✓3)² + 2✓3 + (1)²- 4✓3

=(✓3)²+(1)²-2✓3

=(✓3-1)²

Quadratic formula= (-b+-✓b²-4ac)/2a

Substitute the values of a, b and c

- -(✓3+1) +-✓(✓3-1)²

Or, +(✓3+1) +- (✓3-1) /2

First we take,

(✓3+1+✓3-1) /2

2✓3/2

2 gets cancelled

Therefore one root for the equation is ✓3.

Next we take,

✓3+1-(✓3-1) /2

✓3+1-✓3+1 /2

✓3 gets cancelled

2/2

1

So the second root for the equation is 1.

Hope this helps!!!