Manipal MET2019MathematicsQuadratic Equation

The value of a(a b) for which the sum of the cubes of the roots of x^2-(a-2) x+(a-3)=0 assumes the least value, is

Options

A3
B4
C5
DNone of the above

Correct answer

A. 3

Step-by-step solution

Let and be the roots of the equation aligned & x^2-(a-2) x+(a-3)=0 & + =(a-2) and =a-3 aligned Now, ^3+ ^3=( + )^3-3 ( + ) gathered =(a-2)^3-3(a-3)(a-2) =a^3-9 a^2+27 a-26=(a-3)^3+1 gathered It assumes the least value, if (a-3)^3=0 a=3

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