Question

100x^2-20x+1=0. Find the roots of the following by completing square

Answer 1

Step-by-step explanation:

According to the identity (a-b)²=a²-2ab+b²,

100x²-20x+1 is a square of 20x-1.

(20x-1)²=0

According to the definition of the square root,

20x-1=0

Hence the answer is x=1/20

Answer 2

$\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}$

100x^2-20x+1=0. Find the roots of the following by completing square.

$\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}$

$x= \frac{1}{10} \: or \: x = \frac{1}{10}$

Step-by-step explanation:

$1000 {x}^{2} - 20x + 1 = 0 \\ = 100 {x }^{2} - 10x - 10x + 1 \\ = 10x(10x - 1) - 1(10x - 1) \\ = {(10x - 1)}^{2}$

Roots of this equation are the values of which :-

$⟹( {10x - 1}^{2} ) = 0 \\⟹(10x - 1)(10x - 1) = 0 \\ ∴ \: (10x - 1) = 0 \: \: or \: (10x - 1) = 0$

$x= \frac{1}{10} \: or \: x = \frac{1}{10}$

$\color{red}{About \:Quadratic \: polynomials\: :-}$

➯ A polynomial having degree 2 is called a quadratic polynomial.

➯ The form of quadratic polynomial is

$p(x) = a {x}^{2} + bx + c$

➯ Degree of the quadratic polynomial will be 2.

➯ Variable of the quadratic polynomial will be 1.

$\color{red}{For \:example :-}$

$p(x) = 2 {x}^{2} + 5x + 3 \\ 3 \:➝ \: constant \\ 2 \: and \: 5 \: ➝ \: coefficient \\ {}^{2} \: ➝ \: degree \\ x \:➝ \: variable \:$

➯ In a quadratic polynomial there are 2 zeros because it has degree 2.

$\color{red}{➯ The \: 2\: zeros \:are :-}$

$i) \: \: alpha( \alpha ) \: \\ ii) \: beta \: ( \beta )$

$\color{red}{For \:example :-}$

$p(x) = 2 {x}^{2} + 5 + 3 \\ = 2 {x}^{2} + 2x + 3x + 3 \\ = 2x(x + 1) + 3(x + 1) \\ = (x + 1)(2x + 3) \\ \\ As, \: \: p(x) = 0 \\ \\ ❥∴ \: (x + 1)(2x + 3) = 0 \\ x + 1 = 0 \\ x = - 1 \\ \\ ❥ \: 2x + 3 = 0 \\ 2x = - 3 \\ x = \frac{ - 3}{2} \\ \\ Here, \: \alpha = - 1 \\ \beta = \frac{ - 3}{2}$