According to the fundamental theorem of algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0

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

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