Factorize x^2-4x+1 and also find its zero

1.	Factorize x^2-4x+1 and also find its zero
Answer» Answer:- →x²-4x+1=0 ๛S=-4[Sum of EQUATION] ๛P=1[Product of Equation] [•°• There is no COMMON factor we will use DISCRIMINANT FORMULA] →d=b²-4ac a=1,b=-4,c=1 →d=(-4)²-4×1×1 →d=16-4 →d=12 →√d=±√12 →√d=±2√3 [♦Refer ATTACHMENT for √12 factorization♦] $\rule{200}{1}$ ๛Taking X(+)= $\frac{-b+\sqrt{d}}{2a}$ ๛x= $\frac{-(-4)+2 \sqrt{3}}{2×1}$ ๛x= $\frac{4+2 \sqrt{3}}{2}$ ๛x= $\frac{\cancel{2}(2+ \sqrt{3})}{\cancel{2}}$ ๛x=2+√3 $\rule{200}{1}$ ๛Taking x(-)= $\frac{-b-\sqrt{d}}{2a}$ ๛x= $\frac{-(-4)-2 \sqrt{3}}{2×1}$ ๛x= $\frac{4-2 \sqrt{3}}{2}$ ๛x= $\frac{\cancel{2}(2- \sqrt{3})}{\cancel{2}}$ ๛x=2-√3 $\rule{200}{2}$ ๛x=2±√3 $\rule{200}{3}$

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