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G(x)= a(x^2+1)-x(a^2+1) find its zeros and …

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G(x)= a(x^2+1)-x(a^2+1) find its zeros and verify the relationship between the co efficients and zeroes.

Posted by Monish Narayanan 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 7 months ago

g(x)=a(x²+1)-x(a²+1)
= ax² + a - a²x - x
=ax² - a²x- x+a
= ax(x - a) - (x - a)

=(x-a)(ax-1)

g(x)=0 if x-a=0 or ax-1=0
Hence zeros of the polynomials are: a and {tex} \frac{1}{a}{/tex}
now,
Sum of the zeros ={tex}\mathrm a+\frac1{\mathrm a}=\frac{\mathrm a^2+1}{\mathrm a}=-\frac{-(\mathrm a^2+1)}{\mathrm a}=-\frac{\mathrm B}{\mathrm A}{/tex}
Product of zeros {tex} = \frac{1}{a}\times a{/tex}=1={tex}\frac aa=\frac CA{/tex}
Hence, the relationship is verified.

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