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Obtain all the zeros of x^4+6x^3+x^2-24x-30 …

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Obtain all the zeros of x^4+6x^3+x^2-24x-30 if 2 zeros are 2 and -5

Posted by Saheb Dutta 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

As x = 2 and -5 are the zeroes of x⁴ + 6x³ + x²- 24x - 20.
{tex}\Rightarrow{/tex} (x - 2) and (x + 5) are two factors of x⁴ + 6x³ + x²-24x - 20
{tex}\Rightarrow{/tex} product of factors is (x - 2) (x + 5) = x² + 3x - 10
Dividing x{tex}^4{/tex} + 6{tex}x^3{/tex}+ {tex}x^2{/tex} - 24x - 20 by {tex}x^2{/tex} + 3x - 10

Dividend = divisor {tex}\times{/tex} quotient + remainder
{tex}\Rightarrow{/tex} x⁴ + 6x³ + x² - 24x - 20 = (x² + 3x -10) (x² + 3x + 2)
= (x - 2) (x + 5) (x + 2) (x + 1)
Hence, other two zeroes are -2 and -1.

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