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| 1. |
find the zeroes of the polynomial ( 6x2-3- 7x) |
| Answer» Let\xa0{tex}P\\left( x \\right) =6{ x }^{ 2 }-7x-3{/tex}We have the zeroes of a polynomial are the values of which satisfy {tex}P\\left( x \\right) =0{/tex}\xa0Now\xa0{tex}P\\left( x \\right) =0{/tex}{tex}\\Rightarrow 6{ x }^{ 2 }-7x-3=0\\\\ \\Rightarrow 6{ x }^{ 2 }-9x+2x-3=0\\\\ \\Rightarrow 3x\\left( 2x-3 \\right) +1\\left( 2x-3 \\right) =0\\\\ \\Rightarrow \\left( 3x+1 \\right) \\left( 2x-3 \\right) =0\\\\ \\Rightarrow 3x+1=0\\quad or\\quad 2x-3=0\\quad \\\\ \\Rightarrow x=\\frac { -1 }{ 3 } ,x=\\frac { 3 }{ 2 } {/tex}Hence zeroes of the given polynomial are\xa0{tex}\\frac { -1 }{ 3 } and\\frac { 3 }{ 2 } {/tex} | |