Question

Find the zeros of the polynomial of \[{{\text{x}}^{\text{2}}}{\text{ + 5x - 204}}\].

Answer 1

Hint: First of all split the middle term in such a way that the product of first and last term can be represented as addition or subtraction of its middle term.

Complete step-by-step answer:
Zeros of polynomial \[{{\text{x}}^{\text{2}}}{\text{ + 5x - 204}}\]
Using common factor method write factor of 204
204=2x2x3x17
Hence factor of \[{\text{ - 204 = (17)( - 12)}}\]
So using factorisation method we get,
\[
  {\text{ = }}{{\text{x}}^{\text{2}}}{\text{ + 17x - 12x - 204}} \\
  {\text{ = x(x + 17) - 12(x + 17)}} \\
  {\text{ = (x - 12)(x + 17)}} \\
 \]
To find zeros of polynomials, we can equate the factor equal to zero.
\[
  {\text{(x - 12)(x + 17) = 0}} \\
  {\text{x = 12}} \\
  {\text{x = - 17}} \\
 \]
Hence , \[{\text{(12, - 17)}}\] are zeros of the polynomial.

Note: Polynomials are the algebraic expressions which consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform the arithmetic operations such as addition, subtraction, multiplication and also positive integer exponents for polynomial expressions but not division by variable.
A factor is a number that divides into another number exactly. To find the common factors of two numbers, you first need to list all the factors of each one and then compare them. If a factor appears in both lists then it is a common factor.