Let’s consider the roots of the quadratic equation to be a and b.
Then, we have
A.M. = \( \dfrac{a+b}{2}=8\)
a+b = 16 ............(1)
G.M. = \( \sqrt{ab}\) = 5
ab = 25 ...........(2)
We know that,
A quadratic equation can be formed as,
x2 – x (Sum of roots) + (Product of roots) = 0
x2 – x (a + b) + (ab) = 0
x2 – 16x + 25 = 0 [Using (1) and (2)]
Therefore, the required quadratic equation is x2 – 16x + 25 = 0
Answered by Abhisek | 1 year agoConstruct a quadratic in x such that A.M. of its roots is A and G.M. is G.
Find the geometric means of the following pairs of numbers:
(i) 2 and 8
(ii) a3b and ab3
(iii) –8 and –2
Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).