Question

If am and hm of the roots of a quadratic equation are 3/2 and 4/3 respectively ,then the equation is

Answer 1

Answer:

x² - 3x + 2 = 0     .

Step-by-step explanation:

Let

roots of equation are x and y then

According to the given condition

A . M = ( x + y ) / 2 = 3/2

This implies

         x + y = 3    ....(1)

And

H . M = 2 / ( 1/x + 1/y) = 4/3

     2xy / x + y = 4/3

Putting value of x + y = 3 we get

   2xy / 3 = 4 / 3

This implies that

    2xy = 4

This implies

        xy = 2             ......(2)

 Equation (1) and (2) implies that

x = 2 and y = 1 or y = 2 and x = 1

So

Roots are 2 and 1

Sum of roots = S = 2 + 1 = 3

And

Product of roots = P = 2(1) = 2

we know that general equation in term of sum and products of roots is

x² - Sx + P = 0

Putting values we get

x² - 3x + 2 = 0     ......(3)

Equation (3) is the required equation