NCERT Class XI Mathematics - Sequences and Series - Solutions
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Question : 66
Total: 106
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
Solution:
Let α & β be the roots of a quadratic equation such that A.M. & G.M.of α, β are 8 and 5 respectively.Since A.M. of the roots α and β =
⇒ 8 =
Since G.M. of the roots α and β =√ α β
⇒ 5 =√ α β
⇒ 25 = αβ ... (ii)
As we know the general form of a quadratic equation, whose roots are α and β is
x 2 x 2
⇒ 8 =
Since G.M. of the roots α and β =
⇒ 5 =
⇒ 25 = αβ ... (ii)
As we know the general form of a quadratic equation, whose roots are α and β is
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