Q54 / 160 · AP EAMCET 2018 (22 Apr Shift 1) · Mathematics

If the sum of two roots of the equation $x^3-2 p x^2+3 q x-4 r=0$ is zero, then the value of $r$ is

  • Correct answer
    A
    $\frac{3 p q}{2}$
  • B
    $\frac{3 p q}{4}$
  • C
    $p q$
  • D
    $2 p q$

Solution

Let the two roots of equation is $m,-m$. Now, sum of three roots $=2 p$ Hence, third root will be $2 p$. Now, $m \times(-m)+m \times(2 p)+(-m) \times 2 p=3 q$ $$ \Rightarrow \quad-m^2=3 q $$ Now, $\quad m \times(-n) \times 2 p=4 r$ $$ \begin{array}{rlrl} \Rightarrow & 3 q \times 2 p & =4 r \\ & \Rightarrow & r & =\frac{3 p q \times 2}{4} \Rightarrow r=\frac{3 p q}{2} \end{array} $$

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

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