Write the quadratic equation the arithmetic and geometric means of who

1.	Write the quadratic equation the arithmetic and geometric means of whose roots are A and G respectively.
Answer» Let two roots be a and b ∴ The arithmetic mean is given by \(\frac{a+b}{2}\) ⇒ A = \(\frac{a+b}{2}\) ⇒ Geometric mean is given by √a.b ⇒ G = √a.b Quadratic equation can be written as ⇒ x² - (a + b)x + ab = 0 Where a and b are roots of given equation Substituting AM and GM ⇒ x²-2Ax+G² = 0.

Write the quadratic equation the arithmetic and geometric means of whose roots are A and G respectively.

Answer»

Let two roots be a and b

∴ The arithmetic mean is given by \(\frac{a+b}{2}\)

⇒ A = \(\frac{a+b}{2}\)

⇒ Geometric mean is given by √a.b

⇒ G = √a.b

Quadratic equation can be written as

⇒ x² - (a + b)x + ab = 0

Where a and b are roots of given equation

Substituting AM and GM

⇒ x²-2Ax+G² = 0.