Question

How do you find the standard form of the following quadratic equations and identify the constants a, b, and c $x - 5{x^2} = 10$?

Answer 1

In order to solve this question first, we write the given quadratic equation in standard form by comparing it with the standard equation. Then we again compare all the terms separately and find the value of all the asked variables. example: we compare the coefficient of ${x^2}$ and find the value of the coefficient. And similarly, we find more values.

Complete step by step answer:
We have given a quadratic equation in $x - 5{x^2} = 10$ format.
To convert this in standard form first we write ${x^2}$ and then $x$ and then a constant term.
The standard form of the quadratic equation is $a{x^2} + bx + c = 0$. So, express the equation in this format.
The standard form of the equation is $- 5{x^2} + x - 10 = 0$
On comparing the standard equation then we find the value of a, b, and c.
a is the coefficient of ${x^2}$ is the quadratic equation.
b is the coefficient of $x$in the quadratic equation.
c is the constant term in the quadratic equation.
On comparing the equation we get the value of a, b, and c;
$a = - 5$ a is coefficient of ${x^2}$
$b = 1$ b is coefficient of $x$
$c = - 10$ c is the constant term.

Note: These types of questions are very basic. In these questions, we have to just compare the coefficients with the standard equation. Any equation which has only power 1 with many variables is known as a linear equation. Any equation with power 2 with more variables is known as a quadratic equation. The 3-degree equation is known as cubic and so on.