Question

One zero of the polynomial 3x³ + 16x² +15x -18 is 2/3. Find the other zeros of the polynomial.

Answer 1

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

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