Question

Find the zeroes of the polynomial: $3{x^2} - x - 4$.

Answer 1

Hint: To find the zeros of the polynomial substitute the equation equal to zero and then solve the equation using the mid-term break formula.
Zeros of Polynomials are the real upsides of the variable for which the worth of the polynomial becomes zero. Along these lines, real numbers, 'm' and 'n' are zeroes of a polynomial $p(x),$ if $p(m) = 0$ and $p(n) = 0$.
So, in this question, we will be using the above concept to solve the equation.
The formula used: The formula or the concept used will be a mid-term break and the concept says that In Quadratic Factorization using Splitting of Middle Term which is x term is the amount of two components and item equivalent to the last term.
 \[1^{st} \] and the last term two new factors, including the proper signs.

Complete step-by-step solution:
 $3{x^2} - x - 4$
We use the mid-term split formula,
We get,
\[3{x^2} - 4x + 3x - 4 = 0\]
Now taking out the common term from the paired variables we get,
 \[x(3x - 4) + 1(3x - 4) = 0\]
Now keeping the terms which are the same together and the terms which are different together we get,
\[(3x - 4)(x + 1) = 0\]
Now if we substitute each term to zero we may find the zeros of the given polynomial equation.
\[(3x - 4) = 0,(x + 1) = 0\]
$3x = 4,x = - 1$
So, the zeroes of the given polynomial are \[x\]= $\dfrac{4}{3}$ and \[x = - 1\]

Note: While applying the mid-term break keep the use of proper symbols in mind else the answer might get wrong as this is the most common mistake in which students get the factors but forget the use of the proper sign. Also we are able to use the quadratic formula to solve the given.