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Find the zeroes of the polynomial …

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Find the zeroes of the polynomial x×4+5x×3+2x×2+10x_8isvgiven that two of its zeroes are _roote and root2

    • Posted by Abhi Abhi 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 5 months ago

    Given polynomial, x4 - 5x3 + 2x2 + 10x - 8.
    We have two zeros {tex}\sqrt { 2 }\; \text { and } - \sqrt { 2 }{/tex}.
    {tex}\therefore{/tex}Two factors are (x + {tex}\sqrt 2{/tex} ) and (x - {tex}\sqrt 2{/tex} )
    g(x) = (x + {tex}\sqrt 2{/tex} ) (x - {tex}\sqrt 2{/tex} ) = x2 - 2 is a factor of the given polynomial

    Quotient = x2 - 5x + 4 {tex}= (x - 4)(x - 1){/tex}
    To get other zeroes, equate quotient =0
    {tex}\Rightarrow (x - 4)(x - 1)=0\\\Rightarrow x=4,x=1{/tex}
    Hence, other zeroes are 4 and 1.

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