Question

if one zero of the polynomial $x^{2}$-4x+1 is 2+$\sqrt{3$ , write the other zero

Answer 1

Hey mate!!

Your answer is 2-√3

x²-4x+1=0

here a=1 b=-4 c=1

using the quadratic formula -b±√(b²-4ac)/2a

=> -(-4)±√((-4)²-4(1)(1))/2(1)

=> 4±√(16-4)/2

=> 4±√12/2

=> 4±2√3/2      

=> 2(2±√3)/2      (taking 2 common)

=> 2±√3             (cancelling 2 from the numerator and denominator)

=> 2+√3   2-√3

Therefore, the zeroes of the polynomial is 2+√3 and 2-√3

Hope it helped you....