All the real zeros of the given polynomial are integers.

percibaa8

percibaa8

Answered question

2021-12-17

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.
P(x)=x45x2+4

Answer & Explanation

Cassandra Ramirez

Cassandra Ramirez

Beginner2021-12-18Added 30 answers

Step 1
To find the zeroes of the given polynomial:
P(x)=x45x2+4
For finding zeroes, substituting P(x)=0
P(x)=0
x45x2+4=0
x44x2x2+4=0
x2(x24)(x24)=0
(x24)(x21)=0
(x24)=0, or, (x21)=0
x2=4, or, x2=1
x=±4, or x=±1
x=±2, or x=±1
Required zeroes are: x={±1,±2}.
Step 2
From above,
x45x2+4=(x21)(x24)
x45x2+4=(x+1)(x1)(x+2)(x2)
(using, (a2b2)=(a+b)(ab))
Required factorized form is:
x45x2+4=(x+1)(x1)(x+2)(x2)

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