Question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

Answer 1

According to fundamental theory number of roots is equal to the highest index of X ( or the variable ) with non zero coefficient.
So given eqn has three roots because it is three degree polynomial. Roots are -7/9 , -1/4 , -4/3 .

Answer 2

Given:

$(9x + 7) \times (4x + 1) \times (3x + 4) = 0$

To find:

The number of roots exist for the polynomial function

Answer:

Given Equation is $(9x + 7) \times (4x + 1) \times (3x + 4) = 0$

According to the Zero product rule A \times B=0

Then A=0 and B=0

As per above formula

$(9x + 7) \times (4x + 1) \times (3x + 4) = 0$

$(9x + 7) = 0 \Rightarrow x = \frac {-7}{9}$

$(4x + 1) = 0 \Rightarrow x= \frac {-1}{4}$

$(3x + 4) = 0 \Rightarrow x= \frac {-4}{3}$

3 roots are there in the given polynomial $(9x + 7) \times (4x + 1) \times (3x + 4) = 0$