Question

Use the quadratic polynomial x2+x−12 to answer the questions. A: Which summary correctly applies the Fundamental Theorem of Algebra to the quadratic polynomial? B: Which statement correctly verifies the application of the Fundamental Theorem of Algebra? Select one answer for question A, and select one answer for question B. A: This polynomial has a degree of 2, so the equation x2+x−12=0 has exactly two roots. B: The quadratic equation x2+x−12=0 has two real solutions, x=3 or x=−4, and therefore has two real roots. A: This polynomial has a degree of 2, so the equation x2+x−12=0 has two or fewer roots. A: This polynomial has a degree of 2, so the equation x2+x−12=0 has more than two roots. B: The quadratic equation x2+x−12=0 has two real solutions, x=−3 or x=4, and therefore has two roots. B: The quadratic equation x2+x−12=0 has one real solution, x=3, and therefore has one real root with a multiplicity of 2.

Answer 1

It can be concluded that this polynomial has a degree of 2, so the equation x²+x−12=0 has exactly two root

Explanation:

Given the quadratic polynomial x²+x−12, the highest power in the quadratic polynomial gives its degree. The degree of this quadratic polynomial is therefore 2. This means that the equation has exactly two solutions.

Let us determine the nature of the roots by factorizing the quadratic polynomial and finding the roots.

x²+x−12 = 0

x²+4x-3x−12 = 0

= (x²+4x)-(3x−12) = 0

= x(x+4)-3(x+4) = 0

= (x-3)(x+4) = 0

x-3 = 0 and x+4 = 0

x = 3 and -4

This shows that the quadratic polynomial has two real roots

It can be concluded that this polynomial has a degree of 2, so the equation x²+x−12=0 has exactly two roots