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AP EAMCET20225 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

If one root of the cubic equation x^3+36=7 x^2 is double of another, then the number of negative roots are

Options

  1. A1
  2. B2
  3. C3
  4. D0

Correct answer

A. 1

Step-by-step solution

Let a, 2 a and b be roots of the cubic equation x^3+36-7 x^2=0 So, sum of roots =- (-7) 1 a+2 a+b=7 3 a+b=7 ...(i) Now, a(2 a) b=36 [ . product of roots .= d a ]2 a^2 b=36 and a b+a(2 a)+2 a(b)=0 aligned & & 2 a^2+3 a b & =0 a(2 a+3 b)=0 & & b & = -2 a 3 aligned 3 a- 2 a 3 =7 [from Eq. (i)] 9 a-2 a 3 =7 9 a-2 a=21 7 a=21 a=3 and b=7-3 a=7-3(3)=-2 [from Eq. (i)] Roots are 3,6,-2 Number of negative root is 1 .

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