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Home » Find the zeroes of the following polynomials by factorisation method. 3×2 + 4x – 4
Find the zeroes of the following polynomials by factorisation method. 3×2 + 4x – 4
CBSE | Class 10 | Exercise 2.3 | Maths | NCERT Exemplar | Polynomials
Find the zeroes of the following polynomials by factorisation method. 3×2 + 4x – 4

    \[3x2\text{ }+\text{ }4x\text{ }\text{ }4\]

Parting the center term, we get,

    \[3x2\text{ }+\text{ }6x\text{ }\text{ }2x\text{ }\text{ }4\]

Taking the normal factors out, we get,

    \[3x\left( x+2 \right)\text{ }-\text{ }2\left( x+2 \right)\]

On gathering, we get,

    \[\left( x+2 \right)\left( 3x-2 \right)\]

Thus, the zeroes are,

x+2=0 ⇒ x= – 2

3x-2=0⇒ 3x=2⇒x=2/3

In this manner, zeroes are (2/3) and – 2

Confirmation:

Amount of the zeroes = – (coefficient of x) ÷ coefficient of x2

    \[\alpha \text{ }+\text{ }\beta \text{ }=\text{ }\text{ }b/a\]

    \[\text{ }2\text{ }+\text{ }\left( 2/3 \right)\text{ }=\text{ }\text{ }\left( 4 \right)/3\]

    \[=\text{ }\text{ }4/3\text{ }=\text{ }\text{ }4/3\]

Result of the zeroes = consistent term ÷ coefficient of x2

    \[\alpha \text{ }\beta \text{ }=\text{ }c/a\]

Result of the zeroes = (- 2) (2/3) = – 4/3

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