Question

$\huge\bold\red{Question:-}$
If A.M and G.M of roots of a equation are 8 and 5, respectively, then obtain the quadratic equation.​

Answer 1

SOLUTION:-

Here is your answer,✔️

Answer 2

$\huge\bold\red{Answer:-}$

Let the root of quadratic be a and b.

According to the given condition,

$A.M = \frac{a + b}{2} = 8 = > a + b = 16...(1)$

$G.M = \sqrt{ab} = 5 = > 25...(2)$

The Quadration is given by [tex] X^2[/tex] a€" X

(Sum of root) + (Product of roots) = 0 €"$X^2$ a€"

X (a+b) + (ab) = 0 $X^2$ 16 × + 25 = 0

[ using (1) and (2) ]

$\huge\bold\red{</strong><strong>T</strong><strong>h</strong><strong>u</strong><strong>s</strong><strong>,</strong><strong>}$

The required quation is $X^2$ 16 × + 25 = 0