Question

Using the following diagram:polynomial is 4x^2 + 3x – 7, with 4x^2, 3x, and 7 marked as "terms", 4x^2 marked as the "leading term", and 7 marked as the "constant term", the leading term has the highest degree. The degree of this polynomial is 2. How many solutions does this polynomial have?


a. 0


b. 1


c. 2


d. 3

Answer 1

Option C

2 solutions

Explanation:

We have a polynomial of degree 2.  The leading term is having degree 2 and degree is 2.

so this is a quadratic equation, and has 2 solutions.

The solutions are :

Let us complete the square by

$4x^2+3x-7 = (2x)^2+2(2x)(3/4)+9/16-9/16\\= (2x+3/4)^2-9/16+7$

= 0

Or [tex](2x+3/4)^2 = 9/16+7  = 121/16

Take square root

2x+3/4 = +11/4 or -11/4

Or 2x= 8/4 or -14/4

x = 1 or x = -7/4

are the two solutions.