The number of zeroes that polynomial f(x) = (x – 2)2 + 4 can have is:
Answers
Answer:
0
Step-by-step explanation:
Method 1
(x-2)²+4= (x-2)²+2²
To find the zeroes,
(x-2)²+2²=0
But, the sum of two perfect squares is zero if each of them is zero.
Therefore, p(x) has no zero.
Method 2
(x-2)²+4=(x²-4x+4)+4
By splitting the middle term,
=(x²-2x-2x+4)+4
=(x(x-2)-2(x-2))+4
={(x-2)(x-2)}+4
f(x)=g(x).q(x)+r(x)
Here,
g(x)=(x-2),
q(x)=(x-2)
r(x)=4
g(x) is not the factor of f(x)
Hence, there is no zero for the polynomial.
Answer:
The number of zeroes of the polynomial f(x) = (x-2)^2 + 4 of second degree are 2.
Step-by-step explanation:
- Polynomial:
An expression that contains a combination of variables
and constants with mathematical operations.
Example: ax+b, 3x^2+5x+4 etc.
- Degree of a polynomial:
The highest power of the variable in a polynomial is the degree
of a polynomial.
- Zeroes of a polynomial:
The number of zeroes of a polynomial is the value of a degree
of the polynomial.
Given polynomial is
f(x) = (x-2)^2 + 4
The above polynomial has a degree =2
So, the polynomial (x-2)^2 + 4 have 2 zeroes.
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