Find a palynomial with integer coesficient that Satisfies he gaven conditions P has degree 2 and zeros 3t and 3- 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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I'm unsure of how to work a problem like this

Find a
palynomial with integer coesficient that
Satisfies he gaven conditions
P has degree 2
and zeros 3t and 3-
1
Transcribed Image Text:Find a palynomial with integer coesficient that Satisfies he gaven conditions P has degree 2 and zeros 3t and 3- 1
Expert Solution
Step 1

We need to find a 2-degree polynomial having zeroes at

a 3
B 3 - i
Let the 2 degree polynomial be,
P(x)= ax2bx+ c
,where a, b and c are integers
We know that, for a 2 - degree polynomial
b
b
(3 (3 i)
sum of roots,
a
a
b
6
a
-(1)
b 6a
=>
=> (3 i)(3 i)
product of roots,
aB
a.
C
(3)2 (i)29-(-1)
a.
c = 10a
(2)
=>
substituting the value of b and c from (1) and (2), we get
ax26ax + 10a
P(x)
or, P(x) a(x2 - 6x + 10)
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