To find: The quadratic equation.
Given:
(i) AM of roots of quadratic equation is 10
(ii) GM of roots of quadratic equation is 8
Formula used: (i) Arithmetic mean between a and b = \(\frac{a + b}{2}\)
(ii) Geometric mean between a and b = \(\sqrt{ab}\)
Let the roots be p and q
Arithmetic mean of roots p and q = \(\frac{p+q}{2} = 10\)
\(\frac{p+q}{2} = 10\)
⇒ p + q = 20 = sum of roots … (i)
Geometric mean of roots p and q = \(\sqrt{Pq}\) = 8
⇒ pq = 64 = product of roots … (ii)
Quadratic equation = x2 – (sum of roots)x + (product of roots)
From equation (i) and (ii) Quadratic equation
= x2 – (20)x + (64)
= x2 –20x + 64
x2 –20x + 64