Question

One zero of the polynomial

$3x {}^{2} \: + 16x {}^{2} \: + \: 15x \: - \: 18 \:$
is 2 / 3 . Find the other zeroes

Answer 1

$\bold{Answer :}$

Since, 2/3 is a zero of the given polynomial, (3x - 2) is a factor of it.

Now,

3x³ + 16x² + 15x - 18

= 3x³ - 2x² + 18x² - 12x + 27x - 18

= x² (3x - 2) + 6x (3x - 2) + 9 (3x - 2)

= (3x - 2) (x² + 6x + 9)

= (3x - 2) (x + 3)²

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

So, all the factors of the given polynomial are (3x - 2), (x + 3) and (x + 3)

Therefore, all its zeroes are 2/3, (- 3) and (- 3).

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