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Factorise the Expression F (X) = 2x3 – 7x2 – 3x + 18. Hence, Find All Possible Values of X for Which F(X) = 0. - ICSE Class 10 - Mathematics

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Question

Factorise the expression f (x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.

Solution

f(x)=2x^3-7x^2-3x+18 

for x =2, 

`f(x)=f(2)=2(2)^3-7(2)^2-3(2)+18`  

`=16-28-6+18=0` 

`"Hence, (x-2) is a factor of f(x) "`    

 

∴ `2x^3-7x^2-3x+18=(x-2)(2x^2-3x-9)` 

                              =`(x-2)(2x^2-6x+3x-9) `

                              =`(x-2)[2x(x-3)+3(x-3)]` 

                              =`(x-2,(x-3)(2x+3)`  

now, f(x)=0 

⇒`2x^3-7x^2-3x+18=0` 

⇒`(x-2)(x-3)(2x+3)=0` 

⇒`x=2, 3, (-3)/2`

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Solution Factorise the Expression F (X) = 2x3 – 7x2 – 3x + 18. Hence, Find All Possible Values of X for Which F(X) = 0. Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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