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AP EAMCET202418 May 2024Morning ShiftMathematicsQuadratic EquationActual

If the sum of two roots , of the equation x^4-x^3-8 x^2+2 x+12=0 is zero and , ( ) are its other roots, then 3 +2 =

Options

  1. A0
  2. B1
  3. C3
  4. D5

Correct answer

D. 5

Step-by-step solution

Given , , and be the roots of x^4-x^3-8 x^2+2 x+12=0 . So, such that + =0 aligned & x^4-x^3-8 x^2+2 x+12= (x^2+a ) (x^2-x+b ) & =x^4-x^3+(a+b) x^2-a x+a b aligned After equating co-efficient of x and constant term, we get aligned & -a=2 a=-2 and a b=12 -2 b=12 b=-6 & So, x^4-x^3-8 x^2+2 x+12= (x^2-2 ) (x^2-x-6 ) & = (x^2-2 )(x-3)(x+2) aligned hence, =3, =-2( ) Now, 3 +2 =9-4=5

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