The harmonic mean of two numbers is -frac{8}{ | vedclass

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(B) Let the two numbers be $a$ and $b$.Given,Geometric Mean ($G$.$M$.) $= \sqrt{ab} = 2$,so $ab = 4$ (Eq. $i$).Harmonic Mean ($H$.$M$.) $= \frac{2ab}{

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$x^2+10x+16=0$

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(B) Let the two numbers be $a$ and $b$.Given,Geometric Mean ($G$.$M$.) $= \sqrt{ab} = 2$,so $ab = 4$ (Eq. $i$).Harmonic Mean ($H$.$M$.) $= \frac{2ab}{a+b} = -\frac{8}{5}$.Substituting $ab = 4$ into the $H$.$M$. formula:$\frac{2(4)}{a+b} = -\frac{8}{5} \implies \frac{8}{a+b} = -\frac{8}{5} \implies a+b = -5$.The roots of the required quadratic equation are $2a$ and $2b$.Sum of roots $= 2a + 2b = 2(a+b) = 2(-5) = -10$.Product of roots $= (2a)(2b) = 4ab = 4(4) = 16$.The quadratic equation is given by $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Therefore,$x^2 - (-10)x + 16 = 0$,which simplifies to $x^2 + 10x + 16 = 0$.

The harmonic mean of two numbers is $-\frac{8}{5}$ and their geometric mean is $2$. The quadratic equation whose roots are twice those numbers is

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