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One zero of polynomial 3x³ +16x²+15x-18 is 2/3find other zeroes of polynomial |
| Answer» The given polynomial p(x)=3x3+16x2+15x-18Since\xa0{tex}\\frac { 2 } { 3 }{/tex} is a zero of p(x), so\xa0{tex}\\left( x - \\frac { 2 } { 3 } \\right){/tex} is a factor of p(x).{tex}\\Rightarrow{/tex}\xa0(3x - 2) is also factor of p(x)On dividing p(x) by (3x - 2) , we getSo f(x)=(3x-2)(x2+6x+9)= (x2\xa0+ 3x + 3x + 9)(3x - 2)=[x(x+3)+3(x+3)](3x-2)= (x + 3)(x + 3)(3x - 2){tex}\\therefore{/tex}\xa0x = -3 or x = -3 or x =\xa0{tex}\\frac { 2 } { 3 }{/tex}Thus, the other two zeros are -3, -3. | |