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KCET2013MathematicsQuadratic Equation

If the roots of the equation x³+a x²+b x+c=0 are in AP , then 2 a³-9 a b is equal to

Options

  1. A9 c
  2. B18 c
  3. C27 c
  4. D-27 c

Correct answer

D. -27 c

Step-by-step solution

Given equation is x³+a x²+b x+c=0 Let ( , , ) be the roots of the given equation then according to given condition, we have 2 = + ...(i)( , , are in AP) array ll Now, & + + =-a & +2 =-a (Using Eq. (i) & =- a 3 array Since, is a root of given equation. array lc So, & ³+a ²+b +c=0 & (- a 3 )³+a ( -a 3 )²+b ( -a 3 )+c=0 & - a³ 27 + a³ 9 - a b 3 +c=0 & -a³+3 a³-9 a b+27 c=0 & 2 a³-9 a b+27 c=0 array

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