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According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

(9x + 7)(4x + 1)(3x + 4) = 0

User Jithesh Kt
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2 Answers

4 votes
three! -7/9, -1/4, and -4/3
User MarkusParker
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3 votes

Answer with Step-by-step explanation:

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number can be considered a complex number with its imaginary part equal to zero.

Hence, the given polynomial equation has atleast 1 real root and atmost 3 real roots

(9x + 7)(4x + 1)(3x + 4) = 0

On solving this, we get

9x+7=0 or 4x+1=0 or 3x+4=0

i.e. x= -7/9 or x= -1/4 or x= -4/3

As we can see all the roots are real

Hence, number of real roots are:

3

User Joe Wu
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