Find zeroes of v²+4√3v-15Also verify relationship between the zeroes and the coefficient

Find zeroes of v²+4√3v-15Also verify relationship between the zeroe

1.	Find zeroes of v²+4√3v-15Also verify relationship between the zeroes and the coefficient
Answer» The given quadratic polynomial is: v2\xa0+ 4{tex}\\sqrt 3{/tex}v - 15By factorizing it we have v2\xa0+ 4{tex}\\sqrt 3{/tex}v - 15 = v2\xa0+ 5{tex}\\sqrt 3{/tex}v -\xa0{tex}\\sqrt 3{/tex}v - 15=\xa0v(v\xa0+ 5{tex}\\sqrt 3{/tex})\xa0-\xa0{tex}\\sqrt 3{/tex}(v +\xa05{tex}\\sqrt 3{/tex})\xa0= (v -\xa0{tex}\\sqrt 3{/tex})(v +\xa05{tex}\\sqrt 3{/tex})For zeroes, put the factors equal to zero i.e.,\xa0(v -\xa0{tex}\\sqrt 3{/tex})(v +\xa05{tex}\\sqrt 3{/tex})\xa0= 0{tex}\\Rightarrow v = \\sqrt { 3 } , - 5 \\sqrt { 3 }{/tex}\xa0are zeroes of the polynomial.Verification:\xa0In the given polynomial a = 1, b = 4{tex}\\sqrt 3{/tex}\xa0and c = - 15Now Sum of the zeroes =\xa0{tex}\\sqrt { 3 } + ( - 5 \\sqrt { 3 } ) = - 4 \\sqrt { 3 }{/tex}Also sum of zeroes =\xa0{tex}\\frac { - b } { a }{/tex},\xa0{tex}\\frac { - b } { a } = \\frac { - 4 \\sqrt { 3 } } { a } = - 4 \\sqrt { 3 }{/tex}And product of zeroes =\xa0{tex}\\sqrt { 3 } \\times - 5 \\sqrt { 3 }{/tex}= -15Also,\xa0product of zeroes =\xa0{tex}\\frac { c } { a } = \\frac { - 15 } { 1 } = - 15{/tex}