Question

According to the fundamental theorem of algebra, how many zeros does the function $ f(x) = 3{x^4} + x + 2 $ have ?

Answer 1

Hint: Algebra is an expression in which alphabets are used to represent numbers in a formula or equation involving mathematical operations. A polynomial equation involves alphabets as variables raised to some power and numbers as the coefficient of the variables. The highest exponent of the variable in a polynomial equation is called its degree. Using this information, we can find the number of zeros of the given function.

Complete step-by-step answer:
We have $ f(x) = 3{x^4} + x + 2 $ , in the given function, the powers of x involved are 4 and 1, as 4 is the highest power in the given function, the degree of the function is 4.
Now, according to the Fundamental theorem of algebra, a polynomial equation has as many roots/solutions as the degree of the equation.
Thus the function has 4 roots.
Hence, the function $ f(x) = 3{x^4} + x + 2 $ has 4 zeros.
So, the correct answer is “4”.

Note: The zeros of an equation are the points on the x-axis that is the zeros are simply the x-intercepts. For finding the zeros of a polynomial equation having degree more than 2, we find out the first few zeros by the hit and trial method, and divide the original equation by its factor, so the equation obtained after division is an equation of lesser degree, we keep on dividing the equation by the factors until the obtained equation is of degree 2 whose zeros can be obtained by factoring or completing the square method.