Question

Without actually calculating the zeroes,firm a quadratic polynomial whose zeros are reciprocal of the zeros of the polynomial 5x^2+2x-3

Answer 1

The required quadratic equation would be $3x^2-2x+5=0$

Step-by-step explanation:

Since we have given that

$5x^2+2x-3$

First we find the roots of above quadratic equation:

$5x^2+5x-3x-3=0\\\\5x(x+1)-3(x+1)=0\\\\(x+1)(5x-3)=0\\\\x=-1,x=\dfrac{3}{5}$

So, reciprocals of zeroes would be

$-1,\dfrac{5}{3}$

So, the quadratic equation for the above zeroes would be

$x^-(-1+\dfrac{5}{3})x-1\times \dfrac{5}{3}=0\\\\x^2-(\dfrac{-3+5}{3})x-\dfrac{5}{3}=0\\\\x^2-\dfrac{2}{3}x+\dfrac{5}{3}=0\\\\3x^2-2x+5=0$

Hence, the required quadratic equation would be $3x^2-2x+5=0$

# learn more:

Without actually calculating the zeroes,form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial 5x2+2x-3

https://brainly.in/question/15995881

Answer 2

Answer:

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