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If A.M. and G.M of roots of a quadratic equation are 8 and 5 , respectively, then obtain the quadratic equation.
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Verified Answer
Let $\alpha, \beta$ be the roots of the quadratic equation.
A.M. of $\alpha, \beta=\frac{\alpha+\beta}{2}=8$;
G. M. of $\alpha, \beta=\sqrt{\alpha \beta}=5 \Rightarrow \alpha \beta=5^2$
$\alpha+\beta=16, \alpha \beta=25$
Equation whose roots are $\alpha, \beta$, is $x^2-(\alpha+\beta) x+\alpha \beta=$ 0
$x^2-16 x+25=0$
A.M. of $\alpha, \beta=\frac{\alpha+\beta}{2}=8$;
G. M. of $\alpha, \beta=\sqrt{\alpha \beta}=5 \Rightarrow \alpha \beta=5^2$
$\alpha+\beta=16, \alpha \beta=25$
Equation whose roots are $\alpha, \beta$, is $x^2-(\alpha+\beta) x+\alpha \beta=$ 0
$x^2-16 x+25=0$
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