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Sia ? 6 years, 6 months ago
Let the polynomial is p(x) = 2x4+ 7x3 - 19x2 - 14x + 30
and {tex} \sqrt { 2 } \text { and } - \sqrt { 2 }{/tex} are zeroes of polynomial p(x).
{tex}\therefore ( x - \sqrt { 2 } ) ( x + \sqrt { 2 } ){/tex} = x2 - 2 is a factor of given polynomial.
On dividing given polynomial, we get
quotient : 2x2 + 7x - 15
So, the other factor is 2x2 + 7x - 15
Now, 2x2 + 7x - 15 = 0
{tex}\Rightarrow{/tex} 2x2 + 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}.
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