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One zero of the polynomial 3x^3+ 16x^2 +...

One zero of the polynomial `3x^3+ 16x^2 + 15x -18` is `2/3.`Find the other zeroes of the polynomnial.

Text Solution

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Here, `p(x) = 3x^3+16x^2+15x-18`
One of the zero is `2/3`.
`:. x = 2/3 = 0 => 3x-2 = 0`
If we divide, `p(x)` by `3x-2`, we get, `x^2+6x+9`.
`:. p(x) = (3x-2)(x^2+6x+9)`
`= (3x-2)(x^2+3x+3x+9)`
`= (3x-2)(x(x+3)+3(x+3))`
`=>p(x)= (3x-2)(x+3)(x+3)`
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