Let {a_2},{a_3} in R such that&nbsp | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Apply $\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-\mathrm{R}_{1}$ and $\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-\mathrm{R}_{1}$

$f(x)=-x^{2}+\left(

Vedclass · Accepted Answer

$9$

Vedclass · Answer

Apply $\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-\mathrm{R}_{1}$ and $\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-\mathrm{R}_{1}$

$f(x)=-x^{2}+\left(a_{2}+a_{3}\right) x-a_{2} a_{3}$

$\left|a_{2}-a_{3}\right|=\frac{\sqrt{D}}{|a|}=6=\sqrt{D}=6$

$\max .$ value $=-\frac{D}{4 a}=9$

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} - x}\\
1&{2{a_3} - x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is

Similar Questions

The range of $f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)$ is

The function $f$ satisfies the functional equation $3f(x) + 2f\left( {\frac{{x + 59}}{{x - 1}}} \right) = 10x + 30$ for all real $x \ne 1$. The value of $f(7)$ is

The domain of $f(x) = [\sin x] \cos \left( {\frac{\pi }{{[x - 1]}}} \right)$ is (where $[.]$ denotes $G.I.F.$)

Numerical value of the expression $\left| {\;\frac{{3{x^3} + 1}}{{2{x^2} + 2}}\;} \right|$ for $x = - 3$ is

Show that the function $f: R \rightarrow R$ defined as $f(x)=x^{2},$ is neither one-one nor onto.

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}} 1&{{a_3}}&{{a_2}}\\ 1&{{a_3}}&{2{a_2} - x}\\ 1&{2{a_3} - x}&{{a_2}} \end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is