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Permutations And Combinations

Question

If A.M. and G.M. of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.

Solution

Let a, b be roots of required quadratic equation
Given $fraction numerator straight a plus straight b over denominator 2 end fraction space equals space 8$ and $square root of ab space equals 5$
$rightwards double arrow$ a + b = 16 and ab = 25
S = sum of roots = a + b = 16.
and P = Product of roots = ab = 25
∴ Required quadratic equation is $space space space space space space straight x squared minus Sx plus straight P space equals 0$ or $straight x squared minus 16 straight x plus 25 space equals space 0.$

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Permutations And Combinations

If A.M. and G.M. of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.

Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.

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