If A.M and G.M are roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation

Solution:

Let the roots of the quadratic equations be a and b .

According to the condition,

A.M = (a + b)/2 = 8

⇒ a + b = 16 ....(1)

G.M = √ab = 5

⇒ ab = 25 ....(2)

The quadratic equation is given by,

x² - x (Sum of roots) + (Product of roots) = 0

x² - x (a + b) + (ab) = 0

x² - 16x + 25 = 0 [Using (1) and (2)]

Thus, the required quadratic equation is x² -16x + 25 = 0

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 32

If A.M and G.M are roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation

Summary:

We had to find the quadratic equation in which the A.M and G.M are roots of a quadratic equation are 8 and 5