TS EAMCET · Maths · Quadratic Equation
Two roots of the cubic \(x^3 + 3x^2 + kx = 0\) the value of k is 12 = 0 are real and unequal but have the same absolute value. Then
- A \(4\)
- B \(-4\)
- C \(6\)
- D \(-9\)
Answer & Solution
Correct Answer
(B) \(-4\)
Step-by-step Solution
Detailed explanation
\begin{align*} &\text{Let the roots be } r, -r, \text{ and } t. \text{ Hence, } r - r + t = -3 \Rightarrow t = -3. \\ &\text{Now, the product of the roots is } (r)(-r)(t) = 12. \\ &\Rightarrow -r^2 \cdot (-3) = 12. \\ &\Rightarrow r^2 = 4. \\ &\text{Hence, the roots are } 2, -2,…
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