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Mekhanik [1.2K]
3 years ago
11

Use the quadratic polynomial x2+x−12 to answer the questions. A: Which summary correctly applies the Fundamental Theorem of Alge

bra 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.
Mathematics
1 answer:
Murljashka [212]3 years ago
7 0

Answer:

<h3>It can be concluded that this polynomial has a degree of 2, so the equation x²+x−12=0 has exactly two root</h3>

Step-by-step 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. <u>This means that the equation has exactly two solutions. </u>

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 <u>two real roots</u>

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

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