Higher Math 2nd Paper CQ-Jessore Board-2022

Determine the value of the equation $x^{2}-6 x+25$ $=0$.

If the roots of the equation $f(x)=0$ are real and unequal, then show that the roots of the equation $g(x)=0$ will be imaginary.

If the roots of the equation $M(x)=0$ are in geometric progression, then solve it.

Two unlike parallel forces of agnitude $15 \mathrm{~N}$ and 20 act at two points. What is their resultant?

Prove that, $P-Q=\frac{R}{\sqrt{3}}$.

Determine the position of the pegs.

What is the focus of the parabola $y^{2}-8 x+8 y=0$ ? 2

Determine the equation of the parabola.

Determine the equation of the ellipse.

Determine the value of $\sin ^{-1} \frac{4}{5}+\cos ^{-1} \frac{2}{\sqrt{5}}$

Solve the equation $f(x)+g\left(\frac{\pi}{2}-2 x\right)+f(3 x)=1+$ $g(x)+f\left(\frac{\pi}{2}-2 x\right)$.

Prove that, $2 \tan ^{-1} \frac{\left(\frac{\alpha}{2}\right)}{f\left(\frac{\pi}{2}-\frac{\alpha}{2}\right)} \tan \left(\frac{\pi}{4}-\frac{\beta}{2}\right)=\tan ^{-1}$

Represent $1+2 \mathrm{i}$ in the Argand diagram.

Determine the square root of $M$.

If $p=q$, prove that, $4\left(x^{2}-y^{2}\right)=\frac{a}{x}+\frac{b}{y}$