A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14
<h3>What is a polynomial function?</h3>
A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
x= -2, x=7
Given,
P(x) = 0
This polynomial function has the roots,
x= -2, x=7
So,
(x+2)(x-7)
We have to multiply both of them we get,
P(x)=(x+2)(x-7)
0=x²-5x-14
x²-5x-14=0
Therefore, P(x)=x²-5x-14 is the polynomial function.
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Answer:
For the graph see attached image.
The y-intercept is 2
Step-by-step explanation:
The requested graph of the function is included in the attached image.
The y-intercept can be seen from the image, but also from finding the y-value when x= 0 (zero):
The area is given by
A = (5 + 2x) * (10 + 2x) - 50
Rewriting we have:
A = 50 + 10x + 20x + 4x ^ 2 -50
Rewriting we have:
A = 4x ^ 2 + 30x
Substituting the value of the area we have:
54 = 4x ^ 2 + 30x
Rewriting:
4x ^ 2 + 30x - 54 = 0
We look for the roots:
x1 = -9
x2 = 3/2
We take the positive root:
x2 = 3/2
Answer:
the value of x is:
x = 3/2
