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AP EAMCET2006MathematicsQuadratic Equation

The quadratic equation whose roots are ^2 18^ and ^2 36^ is :

Options

  1. A16 x^2-12 x+1=0
  2. B16 x^2+12 x+1=0
  3. C16 x^2-12 x-1=0
  4. D16 x^2+10 x+1=0

Correct answer

A. 16 x^2-12 x+1=0

Step-by-step solution

Since ^2 18^ and ^2 36^ are the roots of a quadratic equation. Sum of roots = ^2 18^ + ^2 36^ = ( 5 -1 4 )^2+ ( 5 +1 4 )^2= 5+1-2 5 16 + 5+1+2 5 16 = 12 16 = 3 4 and product of roots = ^2 18^ ^2 36^ = ( 5 -1 4 )^2 ( 5 +1 4 )^2= ( 5-1 4 4 )^2= ( 1 4 )^2= 1 16 Required equation whose roots are ^2 18^ and ^2 36^ , is x^2-( sum of roots ) x+( product of roots )=0 x^2- 3 4 x+ 1 16 =0 16 x^2-12 x+1=0

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