Question
Asked Nov 14, 2019
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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
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Find a palynomial with integer coesficient that Satisfies he gaven conditions P has degree 2 and zeros 3t and 3- 1

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Step 1

We need to find a 2-degree poly...

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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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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Math

Calculus