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KCET2024MathematicsSequences and Series

If A M and G M of roots of a quadratic equation are 5 and 4 , respectively, then the quadratic equation is

Options

  1. Ax^2-10 x-16=0
  2. Bx^2+10 x+16=0
  3. Cx^2+10 x-16=0
  4. Dx^2-10 x+16=0

Correct answer

D. x^2-10 x+16=0

Step-by-step solution

Let a and b be the roots the quadratic equation. Then, the quadratic equation is x^2-(a+b) x+a b=0 ....(i) It is given that AM =5 and GM =4 i.e. a+b 2 =5 and a b =4 a+b=10 and a b=16 On substituting these values in Eq. (i), we obtain. Hence, x^2-10 x+16=0 is the required equation.

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