AP EAMCET · Maths · Quadratic Equation
\(f(x)\) is a quadratic expression such that \(f(x)\) is negative when \(x \in\left(-\infty,-\frac{5}{3}\right) \cup(3, \infty)\) and positive when \(x \in\left(-\frac{5}{3}, 3\right) \cdot g(x)\) is another quadratic expression such that \(g(x)\) is negative when \(x \in\left(3, \frac{9}{2}\right)\) and positive when \(x \in R-\left[3, \frac{9}{2}\right]\). Then, the sign of \(f(x) g(x)\) in \([0,5]\) is
- A positive in \(\left[0, \frac{9}{2}\right]\) and negative in \(\left(\frac{9}{2}, 5\right)\)
- B positive in \([0,3) \cup\left(3, \frac{9}{2}\right)\) and negative in \(\left(\frac{9}{2}, 5\right]\)
- C positive in \([0,3) \cup\left(3, \frac{9}{2}\right) \cup\left(\frac{9}{2}, 5\right]\)
- D negative in \([0,3) \cup\left(3, \frac{9}{2}\right) \cup\left(\frac{9}{2}, 5\right]\)
Answer & Solution
Correct Answer
(B) positive in \([0,3) \cup\left(3, \frac{9}{2}\right)\) and negative in \(\left(\frac{9}{2}, 5\right]\)
Step-by-step Solution
Detailed explanation
\(f(x)=a\left(x+\frac{5}{3}\right)(3-x), a>0\) and \(g(x)=b(x-3)\left(x-\frac{9}{2}\right), b>0\) Now, \(f(x) \cdot g(x)=a b\) \[ \left(x+\frac{5}{3}\right)(3-x)(x-3)\left(x-\frac{9}{2}\right) \] According to wavy curve method, So, \(f(x) \cdot g(x)\) is positive in…
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