Math, asked by keshavsoni52387, 9 months ago

EXERCISE 4.2
1. Find the roots of the following quadratic equations by factorisation:
x2-3x - 10=0
(ii) 2x2 + x-6=0
(ii) 2x2 + 7x+5V2 = 0
(iv) 2x2 - x + - = 0
8
(v) 100 x2-20x+1=0​

Answers

Answered by Anonymous
51

Solution:

 \\ \circ \: {\boxed{\tt\green{ Question \ 1}}}

x² – 3x – 10 =0

Taking LHS,

 \colon\implies x² – 5x + 2x – 10

 \colon\implies x(x – 5) + 2(x – 5)

 \colon\implies (x – 5)(x + 2)

The roots of x² – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0 .

As a Result

x – 5 = 0 or x + 2 = 0

 \colon\implies x = 5 or x = -2

 \\ \circ \: {\boxed{\tt\purple{ Question \ 2}}}

2x² + x – 6 = 0

Taking LHS,

 \colon\implies 2x² + 4x – 3x – 6

 \colon\implies 2x(x + 2) – 3(x + 2)

 \colon\implies (x + 2)(2x – 3)

The roots 2x² + x – 6=0 are the values of x for which (x – 5)(x + 2) = 0

As a Result

x + 2 = 0 or 2x – 3 = 0

 \colon\implies x = -2 or {\tt{x = \dfrac{3}{2} }}

 \\ \circ \: {\boxed{\tt\blue{ Question \ 3}}}

√2x² + 7x + 5√2=0

Taking LHS,

 \colon\implies √2x² + 5x + 2x + 5√2

 \colon\implies x(√2x + 5) + √2(√2x + 5)

 \colon\implies (√2x + 5)(x + √2)

The roots of √2x² + 7x + 5√2 = 0 are the values of x for which (x – 5)(x + 2) = 0

As a Result

√2x + 5 = 0 or x + √2 = 0

 \colon\implies x = -5/√2 or x = -√2

 \\ \circ \: {\boxed{\tt\red{ Question \ 4}}}

2x² – x + 1/8 = 0

Taking LHS,

 \colon\implies 1/8 (16x² – 8x + 1)

 \colon\implies 1/8 (16x² – 4x -4x + 1)

 \colon\implies 1/8 (4x(4x – 1) -1(4x – 1))

 \colon\implies 1/8(4x – 1)²

The roots of 2x² – x + 1/8 = 0, are the values of x for which (4x – 1)²= 0

As a Result

(4x – 1) = 0 or (4x – 1) = 0

 \colon\implies x = 1/4 or x = 1/4

 \\ \circ \: {\boxed{\tt\pink{ Question \ 5}}}

100x² – 20x + 1=0

Taking LHS,

 \colon\implies 100x² – 10x – 10x + 1

 \colon\implies 10x(10x – 1) -1(10x – 1)

 \colon\implies (10x – 1)²

The roots 100x² – 20x + 1=0, are the values of x for which (10x – 1)² = 0

 \colon\implies (10x – 1) = 0 or (10x – 1) = 0

 \colon {\tt\bold{ x = \dfrac{1}{10} \: Or \:  x = \dfrac{1}{10} }} \\

Similar questions