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प्रश्न
One zero of the polynomial 3x3 + 16x2 + 15x – 18 is `2/3`. Find the other zeros of the polynomial.
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उत्तर
Given: `x = 2/3` is one of the zero of 3x3 + 16x2 + 15x – 18
Now, we have
`x = 2/3`
⇒ `x - 2/3 = 0`
Now, we divide 3x3 + 16x2 + 15x – 18 by `x - 2/3` to find the quotient
3x2 + 18x + 27
`x - 2/3")"overline(3x^3 + 16x^2 + 15x - 8)`
3x3 – 2x2
– +
18x2 + 15x
18x2 – 12x
– +
27x – 18
27x – 18
– +
X
So, the quotient is 3x2 + 18x + 27
Now, 3x2 + 18x + 27 = 0
⇒ 3x2 + 9x + 9x + 27 = 0
⇒ 3x(x + 3) + 9(x + 3) = 0
⇒ (x + 3) (3x + 9) = 0
⇒ (x + 3) = 0 or (3x + 9) = 0
⇒ x = –3 or x = –3
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