Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function.
$h ( t ) = t ^ { 2 } - 14 t + 49$
A)All Real Zeros: 0, $7$ ; Even multiplicity; number of turning points: 2
B)All Real Zeros: $7$ ; Even multiplicity; number of turning points: 1
C)All Real Zeros: 0, $49$ ; Odd multiplicity; number of turning points: 2
D)All Real Zeros: 0,1, $7$ ; Even multiplicity; number of turning points: 3
E)All Real Zeros: $7$ ; Odd multiplicity; number of turning points: 1

Question

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function. 
 $h ( t ) = t ^ { 2 } - 14 t + 49$  
A)All Real Zeros: 0, $7$ ; Even multiplicity; number of turning points: 2
B)All Real Zeros: $7$ ; Even multiplicity; number of turning points: 1
C)All Real Zeros: 0, $49$ ; Odd multiplicity; number of turning points: 2
D)All Real Zeros: 0,1, $7$ ; Even multiplicity; number of turning points: 3
E)All Real Zeros: $7$ ; Odd multiplicity; number of turning points: 1

Quizplus · Accepted Answer

The given polynomial $h(t) = t^2 - 14t + 49$ can be factored as $(t - 7)^2$, indicating that it has a single real zero at $t = 7$ with even multiplicity (2 in this case). Since it's a quadratic function, it can have at most $n - 1 = 2 - 1 = 1$ turning point, where $n$ is the degree of the polynomial.

Find All the Real Zeros of the Polynomial Function and Determine