AP EAMCET · Maths · Quadratic Equation
The product of all the real roots of the equation \(|x|^2-5|x|+6=0\) is
- A \(25\)
- B \(36\)
- C \(4\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(36\)
Step-by-step Solution
Detailed explanation
Let \(y = |x|\). \(y^2-5y+6=0\) \((y-2)(y-3)=0\) \(y=2\) or \(y=3\) \(|x|=2 \Rightarrow x=\pm2\) \(|x|=3 \Rightarrow x=\pm3\) Roots: \(-3, -2, 2, 3\) Product: \((-3) \times (-2) \times 2 \times 3 = 36\)
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