Question

Find the quadratic polynomial whose zeroes are log 0.5 and log,0.25
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Answer 1

Answer:

The required quadratic polynomial is

$\bf\,x^2-(3\,log\,0.5)x+2(log\,0.5)^2$

Step-by-step explanation:

Let the zeros be

$\alpha=log\,0.5$ and

$\beta=log\,0.25=log\,(0.5)^2=2\,log\,0.5$

The required quadratic polynomial is

$\bf\,x^2-(\alpha+\beta)x+\alpha\,\beta$

$=x^2-(log\,0.5+2\,log\,0.5)x+(log\,0.5)(2\,log\,0.5)$

$=x^2-(3\,log\,0.5)x+2(log\,0.5)^2$

Answer 2

Answer: Our required quadratic equation would be x^2+0.9x+0.18= 0.

Step-by-step explanation:

Since we have given that

First root = log 0.5

Second root = log 0.25

We need to find the quadratic equation.

x^2-(sum of roots )x+ product of roots = 0

x^2-(log 0.5+log 0.25)x + log 0.5× log 0.25=0

x^2-log (0.5×0.25)x+log 0.5× log 0.25= 0

x^2-log 0.125x+ log 0.5× log 0.25= 0

x^2+0.9x+0.18= 0.

Hence, our required quadratic equation would be x^2+0.9x+0.18= 0.