Q54 / 150 · MHT CET 2020 (19 Oct Shift 2) · Mathematics

The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is

  • A
    $x^{2}+68 x-256=0$
  • B
    $x^{2}-68 x-256=0$
  • Correct answer
    C
    $x^{2}-68 x+256=0$
  • D
    $x^{2}+68 x+256=0$

Solution

Quad $E q^{n}: \rightarrow$ $A M \text { of } a, b=34$ $a+b=68$ GM of $a, b,=\pm 6$ $\begin{aligned} a, b \rightarrow \text { roots } \rightarrow \quad a b &=256 \\ x^{2}-68 x+256 &=0 \end{aligned}$

Hence, the correct answer is option: 'C'.

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