Question
Download Solution PDFIf AM and GM of roots of a quadratic equation are 8 and 5 respectively. Find quadratic equation?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If A is the arithmetic mean of numbers a and b and is given by:
If G is the geometric mean of the numbers a and b and is given by:
Calculation:
Let α and β be the two roots of the quadratic equation
Given:
The arithmetic mean of the roots of a quadratic equation is 8
Therefore,
⇒ α + β = 16
Now, geometric mean of the roots of a quadratic equation is 5.
Therefore,
Squaring both sides, we get
⇒ αβ = 25
Thus, the required equation is:
⇒ x2 - (Sum of the roots) x + product of the roots = 0
⇒ Thus, the required equation is:
⇒ x2 - (α + β) x + αβ = 0
⇒ x2 -16x + 25 = 0
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