Question

Write one quadratic polynomial that has one zero.

Answer 1

Answer:

Quadratic polynomial having only one zero: f(x) = (x-1)^2f(x)=(x−1)

2

Solution:

Given that,

We have to write one quadratic polynomial that has one zero

Quadratic polynomial having only one zero:

\begin{lgathered}f(x) = (x-1)^2\\\\f(x) = x^2 - 2x + 1\end{lgathered}

f(x)=(x−1)

2

f(x)=x

2

−2x+1

Find the zeros:

\begin{lgathered}(x-1)^2 = 0\\\\x - 1 = 0\\\\x = 1\end{lgathered}

(x−1)

2

=0

x−1=0

x=1

Thus we get, only one zero at x = 1

Similarly,

We can take any polynomial like: (x-2)^2 , (x-5)^2 , ....(x−2)

2

,(x−5)

2

,...

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Answer 2

(x-5) = (x-5)² is a polynomial that has one zero

• First of all, we need to understand the question very well
• Here we need to write a quadratic expression with both the roots the same.
• It doesn't mean quadratic polynomial with one value for x or a polynomial with both the values of zeroes the same.
• If the polynomial (x-5) = (x-5)² is solved by separately equating it with 0, in both cases x is going to get the same value, which is 5.
• This is not the only polynomial satisfying this condition.
• In the polynomial, if 5 is replaced by values like 1,2,3 etc., still we will have the same value for the x
• #SPJ3