Question

Find the zeroes of the polynomial $2{{x}^{2}}-7x$.

Answer 1

Hint: Start by defining a polynomial and zeros of a polynomial. Equate the given polynomial to 0. Take x common in the LHS. You will then have two options: $x=0\text{ or }\left( 2x-7 \right)=0$ . Solve these to get the values of x which is the final answer.

Complete step-by-step answer:
In this question, we need to find the zeroes of the polynomial $2{{x}^{2}}-7x$.
Let us first define a polynomial.
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Now, we will define zeroes of a polynomial.
For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials. In general, we use to find the zeros of quadratic equations, to get the solutions for the given equation.
Now, we are given the polynomial $2{{x}^{2}}-7x$.
To find zeroes of this polynomial, we will equate it to 0. Doing this, we will get the following:
$2{{x}^{2}}-7x=0$
Now, we need to find the values of x which satisfy the above equation.
From the above equation, take x common on the LHS.
$x\left( 2x-7 \right)=0$
Now, to make this equation equal to 0, we have two options:
$x=0\text{ or }\left( 2x-7 \right)=0$
So, $x=0,\dfrac{7}{2}$
So, the zeros of the given polynomial $2{{x}^{2}}-7x$ are $x=0,\dfrac{7}{2}$.
This is the final answer.

Note: In this question, it is very important to know what a polynomial is and then further what zeros of a polynomial are. Without this knowledge you will not be able to find the solution to this question. Students must remember that for finding zeroes of polynomial we have to equate it to 0. Sometimes students make mistakes for finding zeroes of polynomials by substituting the value of x as 0 which is wrong.