Solution of a Quadratic Equation

Solve for $x$:

$\sqrt{2x+9}+x=13$

Solve the following quadratic equation: $x^2-7x+10=0$.

Solve the following quadratic equation: $x^2-5x+6=0$.

The discriminant of the quadratic equation $x^2-k=0$. where $k$ is a positive number, is

In a garden, trees are planted in rows. The number of trees in each row is $5$ less than the number of rows. If the number of trees planted be $336$, find the number of trees planted in each row.

In a garden trees are planted in rows. The number of trees in each row is $5$ less than the number of rows. If the total number of trees planted be $336$. Find the number of trees planted in each row?

Find the value of the discriminant of the quadratic equation $2x^2-4x+3=0$.

To save fuel, to avoid air pollution and for good health two persons $A$ and $B$ ride bicycle for a distance of $12 \mathrm{km}$ to reach their office. As the cycling speed of $B$ is $2 \mathrm{km}/\mathrm{h}$ more than that of $A, B$ takes $30$ minutes less than that of $A$ to reach the office. Find the time taken by $A$ to reach the office in hours.

If $\left(6x^2-xy\right):\left(2xy-y^2\right)=6:1;$ find $x:y$.

The speed of a boat in still water is$12\mathrm{km}/\mathrm{hr}$. It can go $15\mathrm{km}$ upstream and return downstream to the original point in$2 hours 40 minutes$. Find the speed of the stream.

A two digit number is four times the sum and twice the product of its digits. Find the number.

A two digit number is four times the sum and six times the product of its digits. Find the number.

Factories $x^3-19x+30$

If $x^3-5x^2+7x-2$ is factorised as $(x-k)\left(x^k-\left(k+1\right)x+1\right)$, then find the value of $k$

Note; This question is given in the book seems to have error and the modified question should be as given below.

Two factors of $a{x}^3+b{x}^2+cx-2$  are $(x+1)$and $(2 x+1)$. The remainder when the expression is divided by$x+2$ is$-12$ What is the third factor of the expression?

If  $2x^3-x^2+2x-1$ can be factorised as $\left(kx-1\right)\left(x^k+1\right)$, then find the value of $k$

If $x^3-x^2-x-2$ can be factorised as $(x-k)\left(x^k+x^{k-1}+1\right)$, then find the value of $k$

Factories: $x^3-2x^2-5x+6$

Show that $12x^3+16x^2-5x-3$ is divisible by $2x-1$ and find the factor of the expression.

When the expression $a{x}^3+b{x}^2+x-a$ is exactly divisible by $x+3$ and by $2x-1$, find $a$ and $b$ and the other factor.