Question

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Maths

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Answer 1

Heya !!

Here's your answer..
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Q.(a)

=> Ans.

p(x) 2x⁴ - 3x³ - 5x² + 9x - 3

Given : x = √3 and x = -√3

( x - √3 ) = 0 and ( x + √3 ) = 0

=> ( x-√3 )( x+√3 )

=> ( x² - 3 ) --[ a²-b² = ( a-b )(a+b ) ]


Divide p(x) by x² - 3..,

By dividing it we get 2x² - 3x + 1
[ Division is in the attachment 1 ]

Now factorize 2x² - 3x + 1

2x² - 3x + 1 = 0

2x² - 2x - x + 1 = 0
2x ( x-1 ) -1 ( x-1 ) = 0
( 2x-1 ) ( x-1 ) = 0
( 2x-1 ) = 0 and ( x-1 ) = 0

x = ½ and x = 1
__________________________

Q. (b)

=> Ans.

f(x) = 2x⁴ - 9x³ + 5x² + 3x - 1

Given : x = 2+√3 and x = 2-√3

x - 2 - √3 = 0 and x - 2 + √3 = 0

= {( x - 2 ) - √3 } {( x - 2 ) + √3 }
= ( x - 2 )² - ( √3 )²
= x² - 4x + 4 - 3
= x² - 4x + 1

Divide f(x) by x² - 4x + 1

By dividing it we get 2x² - x - 1
[ Division is in attachment 2 ]

Now factorize 2x² - x - 1

2x² - x - 1 = 0
2x² - 2x + x - 1 = 0
2x ( x-1 ) + 1 ( x-1 ) = 0
( 2x + 1 ) ( x - 1 ) = 0
( 2x + 1 ) = 0 and ( x - 1 ) = 0

x = -½ and x = 1
____________________________

Q.(c)

=> Ans.

p(x) = x² - 11x² + 28

Given : x = √7 and x = -√7
x - √7 = 0 and x + √7 = 0

= ( x-√7 ) ( x+√7 )
= x² - 7

Divide p(x) by x²-7

By dividing it we get x² - 4
[ Division is in attachment 3 ]

x² - 4 = 0
x² = 4
x = √4
x = ± 2
x = +2 and x = -2
__________________________

Hope it helps

Thanks :)