Examine the diagram, where AB←→ is secant to the circle at points A and B, and CD←→ is secant to the circle at points C and D. T
he lines intersect inside the circle at point P, which is not the center.
A circle with no center shown and two secants as described in the text. Segment B P equals 6, segment C P equals 7, and segment D P equals 12.
What is the length of AP¯¯¯¯¯¯¯¯?
Enter the correct value.
A circle with no center shown and two secants as described in the text. Segment B P equals 6, segment C P equals 7, and segment D P equals 12.
What is the length of AP¯¯¯¯¯¯¯¯?
Enter the correct value.
1 answer:
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Answer:
Choice b.
.
Step-by-step explanation:
The highest power of the variable in this polynomial is
. In other words, this polynomial is quadratic.
It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to .)
After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.
Apply the quadratic formula to find the two roots that would set this quadratic polynomial to . The discriminant of this polynomial is
.
.
Similarly:
.
By the Factor Theorem, if is a root of a polynomial, then
would be a factor of that polynomial. Note the minus sign between
and
.
- The root
corresponds to the factor
, which simplifies to
.
- The root
corresponds to the factor
, which simplifies to
.
Verify that indeed expands to the original polynomial:
.