Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determin
1 answer:
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ANSWER TO QUESTION 1
.
EXPLANATION
The function given to us is,
According to rational roots theorem,
are possible rational zeros of
.
We find out that,
Also
This implies that
are factors of
and hence
is also a factor.
We perform the long division as shown in the diagram.
Hence,
.
ANSWER TO QUESTION 2
Sketching the graph
We can see from the factorization that the roots
and
have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.
Also the root has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.
Now we determine the position of the graph on the following intervals,
We can now use these information to sketch the function as shown in diagram
Answer:
We can use the Laws of Exponent to rewrite both sides of the equation:
Let a¹² x a⁴ = a⁸ x a⁸
⇒ a¹²⁺⁴ = a⁸⁺⁸
a¹⁶ = a¹⁶ ✅
⇒ a¹² x a⁴ = a⁸ x a⁸ is true for all values of a.
Explanation:
The equation a¹² x a⁴ = a⁸ x a⁸ is true because, on both the RHS and LHS of the equation, both terms in 'a' have exponents that when added (Law of Multiplication of Exponents) are equal to each other, i.e. 12+4 = 8 + 8.
