Match each polynomial equation to the correct number of roots it has, according to the Fundamental Theorem of

Question

Match each polynomial equation to the correct number of roots it has, according to the Fundamental Theorem of Algebra. The equations are x^2+5x-6=0, x^5+3x^2-10=0, 4x^3-x+2=0, 7x^8-2x^7+x^3=0 and the roots are 2 roots, 5 roots, 3 roots, and 8 roots.

GPT-5 mini · Answer

By the Fundamental Theorem of Algebra (degree = number of complex roots, counting multiplicity):

- x^2 + 5x - 6 = 0 → 2 roots  
- x^5 + 3x^2 - 10 = 0 → 5 roots  
- 4x^3 - x + 2 = 0 → 3 roots  
- 7x^8 - 2x^7 + x^3 = 0 → 8 roots

Match each polynomial equation to the correct number of roots it has, according to the Fundamental Theorem of Algebra. The equations are x^2+5x-6=0, x^5+3x^2-10=0, 4x^3-x+2=0, 7x^8-2x^7+x^3=0 and the roots are 2 roots, 5 roots, 3 roots, and 8 roots.

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