Math, asked by rs3165220, 7 months ago

Page No.
Date
clarksheet-> (4
Fill the racks of the following
quadratic equation by factorisation
100x² - 20x+1=0​

Answers

Answered by harshaprince95g
3

Answer:

........i not understand

Answered by TheEternity
3

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

Find the roots of the given quadratic equation by factorisation. 100x2 – 20x + 1 = 0.

\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}

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