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  • Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial <img alt="f(x)=ax^{2}+bx+c,a\neq 0,c\neq 0" src="https://learn.careers360.com/latex-image/?%5Cinline%20f%28x%29%3Dax%5E%7B2%7D&plus;bx&plus;c%2Ca%5Cne

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x)=ax^{2}+bx+c,a\neq 0,c\neq 0.

 

 

 
 
 
 
 

Answers (1)

\\f(x)=ax^2+bx+c\\\text{let p and q are the roots of the given polynomial}\\\text{sum of the roots}\ p+q=\frac{-b}{a}.........(1)\\\text{product of the roots}\ pq=\frac{c}{a}..........(2)

If the roots of a new polynomial q(x) are reciprocal of roots of f(x), then the roots are 1/p and 1/q

\\\text{sum of the roots of q(x)} =\frac{1}{p}+\frac{1}{q}=\frac{p+q}{pq}=\frac{-b}{c}\ from\ (1)\ and\ (2)\\\\\text{product of the roots}\ \frac{1}{pq}=\frac{a}{c} \ (from\ (2))

So,

q(x)=x^2-(\frac{-b}{c})x+\frac{a}{c}=x^2+(\frac{b}{c})x+\frac{a}{c}

Posted by

Safeer PP

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