Introduction to Quadratic Equations

In a two-digit positive number, the unit digit is equal to the square of ten's digit. The difference between the original number and the number formed by interchanging the digits is $54.$ What is $40\%$ of the original number?

Write a quadratic function $f$ whose zeros are $2$, and $6$.

Write a quadratic function $f$ whose zeros are $3$, and $10$.

If one zero of the quadratic polynomial $x^2-kx+1$ is $1$, then the value of $k$ is

$a{x}^n+bx+c$ is a quadratic polynomial if $n=?$

Which of the following is not a Quadratic equation?

The Quadratic equation, whose roots are  $2+\sqrt{3}$ and $2-\sqrt{3}$ is 

If $p$ and $q$ are the roots of the equation $x^2-3x+2=0$, find the value of $\frac{1}{q}-\frac{1}{p}$.

The sum and product of the zeroes of a quadratic polynomial $p\left(x\right)=a{x}^2+bx+c$ are $-3$ and $2$ respectively.  $b+c=$

If one of the roots of the quadratic equation $x^2–7x+k=0$ is $4$, then find the value of $k$.

Which of the following is not a quadratic equation? 

The standard form of the quadratic equation $\frac{x+1}{2}=\frac{1}{x}$ is

A dealer sells a toy for $₹24$ and gains as much percent as the cost price of the toy. Find the cost price of the toy in rupees.

Find the value of $\left(a-b\right)$ from the quadratic equation $2x^2 – 5x + 7 = 0$, by comparing it with the standard quadratic equation.

From the following equations, which one is the quadratic equation?

I.  \( 35x^4+369x^2+900=0 \)
II.  \( 144y^4+337y^2+144=0 \)

Check whether the equation $x+\frac{1}{x}+x^2, x\ne 0$ is quadratic?

Check whether the equation $x^2+3x+1=(x-2{)}^2$ is quadratic?

Check whether the equation, $(x+2{)}^3=x^3-4$ is quadratic?

Check, whether the equation $x(x+1)+8=(x+2)(x-2)$ is quadratic?