For the polynomial,
P(x)= (a+1)x^3+(b-7)x^2+c+5
find: a, b and c if:
(a) P(x) is monic
(b) the coeffi cient of x^2 is 3
(c) the constant term is -1
(d) P(x) has degree 2
(e) the leading term has a coefficient of 5.
The text book did not explain how to find the values of a,b and c when the polynomial is not in the form of ax^2+bx+c. How would I go about doing this?
P(x)= (a+1)x^3+(b-7)x^2+c+5
find: a, b and c if:
(a) P(x) is monic
(b) the coeffi cient of x^2 is 3
(c) the constant term is -1
(d) P(x) has degree 2
(e) the leading term has a coefficient of 5.
The text book did not explain how to find the values of a,b and c when the polynomial is not in the form of ax^2+bx+c. How would I go about doing this?
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These are not the same a, b, and c as in the quadratic formula
a) Monic means that the leading coefficient is 1, so a + 1 = 1 and a = 0
b) b – 7 = 3, b = 10
c) c + 5 = –1, c = –6
d) The coefficient of x³ is zero, so a = –1
e) a + 1 = 5, a = 4
a) Monic means that the leading coefficient is 1, so a + 1 = 1 and a = 0
b) b – 7 = 3, b = 10
c) c + 5 = –1, c = –6
d) The coefficient of x³ is zero, so a = –1
e) a + 1 = 5, a = 4
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I am not exactly sure what you want. If you want to find a, b, and c such that all five conditions to hold, then you can't. Condition (a) states that P(x) is monic; in other words, the leading term has a coefficient of 1. On the other hand, (e) states that this coefficient is 5.
If you just wanted one condition to hold, then there are not unique values of a, b, and c for each statement to hold.
Can you revise your question?
If you just wanted one condition to hold, then there are not unique values of a, b, and c for each statement to hold.
Can you revise your question?