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प्रश्न
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
उत्तर
Let the root of the quadratic equation be a and b.
According to the given condition,
A.M. = `(a + b)/2 = 8 = a + b = 16` ...(1)
G.M. = `sqrt(ab) = 5 = ab = 25` ...(1)
The quadratic equation is given by,
x2– x (Sum of roots) + (Product of roots) = 0
x2 – x (a + b) + (ab) = 0
x2 – 16x + 25 = 0 [Using (1) and (2)]
Thus, the required quadratic equation is x2 – 16x + 25 = 0
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