Find all the other zeroes of the polynomial p(x) =2xraise to power 4-7xcube +19xsquare - 14x+30

Find all the other zeroes of the polynomial p(x) =2xraise to power 4-7

1.	Find all the other zeroes of the polynomial p(x) =2xraise to power 4-7xcube +19xsquare - 14x+30
Answer» Let the polynomial is p(x) = 2x4+ 7x3\xa0-\xa019x2\xa0- 14x + 30and {tex} \\sqrt { 2 } \\text { and } - \\sqrt { 2 }{/tex}\xa0are zeroes of polynomial p(x).{tex}\\therefore ( x - \\sqrt { 2 } ) ( x + \\sqrt { 2 } ){/tex}\xa0= x2\xa0- 2 is a factor of given polynomial.On dividing given polynomial, we getquotient : 2x2\xa0+ 7x - 15So, the other factor is 2x2\xa0+ 7x - 15Now,\xa02x2\xa0+ 7x - 15 = 0{tex}\\Rightarrow{/tex} 2x2\xa0+ 10x - 3x - 15 = 0{tex}\\Rightarrow{/tex}2x(x + 5) - 3 (x + 5) = 0{tex}\\Rightarrow{/tex}(x + 5)(2x - 3) = 0{tex}\\therefore \\quad x = - 5 , x = \\frac { 3 } { 2 }{/tex}Hence Zeores of given polynomial are {tex}\\sqrt { 2 } , - \\sqrt { 2 } , - 5 \\text { and } \\frac { 3 } { 2 }{/tex}.