Question

If $\left[\begin{array}{ccc}4a^2& 4a& 1\\ 4b^2& 4b& 1\\ 4c^2& 4c& 1\end{array}\right]\left[\begin{array}{c}f(-1)\\ f\left(1\right)\\ f\left(2\right)\end{array}\right]=\left[\begin{array}{c}3a^2+3a\\ 3b^2+3b\\ 3c^2+3c\end{array}\right]$ $f\left(x\right)$ is a quadratic function and its maximum value occurs at a point $V.A$ is a point of intersection of $y=f\left(x\right)$ with $x$ -axis and point $B$ is such that chord $AB$ subtends a right angled at $V.$ Find The area enclosed by $f\left(x\right)$ and chord $AB.$

• A. $\frac{125}{3}$ sq unit
• B. $\frac{115}{3}$ sq unit
• C. $\frac{120}{3}$ sq unit
• D. $\frac{130}{3}$ sq unit

Answer 1

The correct option is A $\frac{125}{3}$ sq unit

Hence, Option (A) is the correct answer.