Q. 134.7( 15 Votes )

# Find all the zeroes of the polynomial 3x^{3} + 10x^{2} – 9x – 4 if one of its zero is 1.

Answer :

Consider 3x^{3} + 10x^{2} – 9x – 4,

Since 1 is the zero of the given polynomial.

So, (x-1) is the factor of the polynomial.

So, 3x^{3} + 10x^{2} – 9x – 4 = (x-1)(3x^{2} + 13x +4)

Now, 3x^{2} + 13x +4 = 3x^{2} + 12x + x +4

= 3x (x + 4) + 1 (x+4)

= (3x+1) (x+4)

So, zeroes will be

Thus, the zeroes will be x = -4, , and 1.

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Find all the zeroes of the polynomial 3x^{3} + 10x^{2} – 9x – 4 if one of its zero is 1.