Factorise 2x sq + 12root 2x+ 35 and find the polynomial whose zeros are twice of the polynomial
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Answered by
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2x² + 12√2x + 35
= 2x² + 7√2x + 5√2x + 35
=√2x ( √2x + 7) +5( √2x + 7)
=( √2x + 5)( √2x + 7)
hence, (√2x + 5) and (√2 + 7) are two factors of 2x² + 12√2x + 35 ,
again ,
a unknown polynomial , whose zeros are 2 times of the given polynomial .
e.g 2 × (-5/√2) and 2 × (-7/√2) are the zeros of unknown polynomial .
so,
polynomial is ,
x²- 2( 5+7)/√2 + 4(5/-√2)(7/-√2)
x² - 12√2x + 70
= 2x² + 7√2x + 5√2x + 35
=√2x ( √2x + 7) +5( √2x + 7)
=( √2x + 5)( √2x + 7)
hence, (√2x + 5) and (√2 + 7) are two factors of 2x² + 12√2x + 35 ,
again ,
a unknown polynomial , whose zeros are 2 times of the given polynomial .
e.g 2 × (-5/√2) and 2 × (-7/√2) are the zeros of unknown polynomial .
so,
polynomial is ,
x²- 2( 5+7)/√2 + 4(5/-√2)(7/-√2)
x² - 12√2x + 70
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