If A.M. and G.M. of roots of a quadratic equa | vedclass

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Question

(A) Let the roots of the quadratic equation be $a$ and $b$.According to the given condition,$A.M. = \frac{a+b}{2} = 8 \Rightarrow a+b = 16$  $(1)$$G.M

Vedclass · Accepted Answer

$x^{2}-16x+25=0$

Vedclass · Answer

(A) Let the roots of the quadratic equation be $a$ and $b$.According to the given condition,$A.M. = \frac{a+b}{2} = 8 \Rightarrow a+b = 16$  $(1)$$G.M. = \sqrt{ab} = 5 \Rightarrow ab = 25$  $(2)$The quadratic equation is given by,$x^{2} - x(	ext{Sum of roots}) + (	ext{Product of roots}) = 0$$x^{2} - x(a+b) + (ab) = 0$Substituting values from $(1)$ and $(2)$,$x^{2} - 16x + 25 = 0$Thus,the required quadratic equation is $x^{2} - 16x + 25 = 0$.

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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