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If 'm' and 'n' are zeroes of the polynomial ax2 -5x + c, find value of 'a' and 'c' when m+n=mn=10

Posted by Akanksha Devgan 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

f(x)=ax² - 5x + c.
as m and n are zeros of polynomial
therefore m + n = {tex}- \frac { ( - 5 ) } { a } = \frac { 5 } { a }{/tex} and mn = {tex}\frac { c } { a }{/tex}
Now, m + n = 10

{tex}\frac 5a{/tex} =10

so a={tex}\frac12{/tex}
also mn =10 ={tex}\frac { c } { a }{/tex}

10a=c

c=10{tex}\times{/tex} {tex}\frac 12=5{/tex}

hence c = 5 and a ={tex}\frac 12{/tex}

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