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AP EAMCET201922 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

If (3 x^2-7 x+2=0 ) and (15 x^2-11 x+a=0 ) have a common root and (a ) is a positive real number, then the sum of the roots of the equation (15 x^2-a x+7=0 ), is

Options

  1. A( 76 15 )
  2. B( 38 15 )
  3. C( 2 15 )
  4. D( 36 15 )

Correct answer

C. ( 2 15 )

Step-by-step solution

Given equations are ( and aligned 3 x^2-7 x+2 & =0 15 x^2-11 x+a & =0 Here, a₁=3, b₁=-7, c₁ & =2 a₂=15, b₂=-11, c₂ & =a aligned ) and Let ( ) is a common root of the Eqs. (i) and (ii), Then, ( ) will satisfy both the equations. ( ) Common root is given by ( aligned & (2 15-a 3)^2=(-7 a+22(-33+105) & (30-3 a)^2=(22-7 a)(72 & [9(10-a)^2 ]=(22-7 a)(72 & (10-a)^2=(22-7 a) 8 & 100+a^2-20 a=176-56 a & a^2+36 a-76=0 & a^2+38 a-2 a-76=0 & a(a+38)-2(a+38)=0 & (a+38)(a-2)=0 & a=2 [ a > 0] aligned ) Now, for equation (15 x^2-

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