Given that √ 2 is a zero of the cubic polynomial 6x3 √ 2 x 2 x 4 √ 2 find its other two zeroes

√2 is zero of 6x³ +√2x² -10x -4√2 ,
So, (x - √2) is a factor of 6x³ + √2x² -10x -4√2 .

6x³ + √2x² -10x -4√2 = 6x³ -6√2x² + 7√2x² -14x + 4x - 4√2= 6x²(x - √2) + 7√2x(x -2) + 4(x -√2) = {6x² + 7√2x + 4}(x - √2)= {6x² + 3√2x + 4√2x + 4}(x -√2)= {3√2x(√2x + 1) + 4(√2x +1)}(x -√2)

= (3√2x +4)(√2x +1)(x - √2)

Hence, two other zeros are -4/3√2, and -1/√2

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Given that √2 is a zero of the cubic polynomial 6x3+√2x2 10x 4√2, find its other two zeroes.

Solution

is a zero of

So,

is a factor of

=

=

=

=

=

=

Hence, two other zeros are

and

Mathematics

RD Sharma

Standard X