
Check whether -2 and 2 are zeroes of the polynomial \[x+2\].
Answer
588.6k+ views
Hint: For the above question we would have to know about the zeroes of the polynomial. The zero of a polynomial can be defined as those values of x when substituted in the polynomial, making it equal to zero. In other words, we can say that the zeroes are the roots of the polynomial. Let us suppose that we have a polynomial P(x) and a is the zero of this polynomial. Then P(a) = 0. We have been asked whether -2 and 2 are zeroes of the above polynomial. So, we have to check if each one makes the value of the polynomial equal to zero or not.
Complete step-by-step answer:
We know that if we have a polynomial P(x) and \[\alpha \] and \[\beta \] are the zeroes of the polynomial. Then,
\[\begin{align}
& P\left( \alpha \right)=0 \\
& P\left( \beta \right)=0 \\
\end{align}\]
So, -2 and 2 are the zeroes of the polynomial \[x+2\] then if we substitute these zeroes in the given polynomial it is equal to zero.
For the zero -2,
\[x+2=(-2)+2=0\]
Hence -2 is the zero of the polynomial.
For the zero 2,
\[x+2=(2)+2=4\ne 0\]
Hence 2 is not the zero of the polynomial.
Therefore, only -2 is the zero of the given polynomial among -2 and 2.
Note: Remember that we can find the zeros of a polynomial P(x) by equating it to zero. \[\Rightarrow P(x)=0\] Also remember that the number of zeroes of the polynomial is equal to the maximum exponent of the variable in the polynomial.
Complete step-by-step answer:
We know that if we have a polynomial P(x) and \[\alpha \] and \[\beta \] are the zeroes of the polynomial. Then,
\[\begin{align}
& P\left( \alpha \right)=0 \\
& P\left( \beta \right)=0 \\
\end{align}\]
So, -2 and 2 are the zeroes of the polynomial \[x+2\] then if we substitute these zeroes in the given polynomial it is equal to zero.
For the zero -2,
\[x+2=(-2)+2=0\]
Hence -2 is the zero of the polynomial.
For the zero 2,
\[x+2=(2)+2=4\ne 0\]
Hence 2 is not the zero of the polynomial.
Therefore, only -2 is the zero of the given polynomial among -2 and 2.
Note: Remember that we can find the zeros of a polynomial P(x) by equating it to zero. \[\Rightarrow P(x)=0\] Also remember that the number of zeroes of the polynomial is equal to the maximum exponent of the variable in the polynomial.
Recently Updated Pages
In cricket, what is a "pink ball" primarily used for?

In cricket, what is the "new ball" phase?

In cricket, what is a "death over"?

What is the "Powerplay" in T20 cricket?

In cricket, what is a "super over"?

In cricket, what is a "tail-ender"?

Trending doubts
Why is there a time difference of about 5 hours between class 10 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who Won 36 Oscar Awards? Record Holder Revealed

The time gap between two sessions of the Parliament class 10 social science CBSE

