Question

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

Answer 1

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

$\rule{200}{3}$

Answer 2

Step-by-step explanation:

GIVEN THE TASK: -

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

SOLUTION:-

${x}^{2} - 4x + 1$

THE QUADRATIC FORMULA IS SIMPLY JUST,

${ax}^{2} + bx + c = 0$

THEN,

$a = 1 \\ b = - 4 \\ c = 1$

On using the quadratic formula,

$x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{ 2a }$

On keeping the mind of A,B and C

in the formula :-

$x = \frac{ - ( - 4 )\frac{ + }{ - } \sqrt{ ( - 4} ) - 4 \times 1 \times 1}{?}$

On solving,

$x = \frac{4 \frac{ + }{ - } \sqrt{16 - 4 } }{2 \times 1} \\ \\ x = \frac{4 \frac{ + }{ - } \sqrt{12} }{2}$

Once the mind of X is plus,

$x = \frac{4 + \sqrt{12} }{2} \\ x = 2 + \sqrt{12}$

Once the mind of x is minus,

$x = \frac{4 - \sqrt{12} }{2} \ \\ \\ \ x = 2 - \sqrt{12}$