Question

Zero of the polynomial p(x) = 3x + 5 is:
A. 0
B. -5
C. $\dfrac{5}{3}$
D. $-\dfrac{5}{3}$

Answer 1

Hint:
1) The values of the variables, for which the value of the expression becomes zero, are called as its zeros / roots.
2) The solutions of an equation are also sometimes called as its zeros or roots.
3) A polynomial / equation of degree n, has at most n roots.
4) To solve a linear equation (degree 1), we try to keep the variable on one side of the equation and move all the numbers on the other side of the equation.

Complete step by step solution:
A zero of the polynomial p(x) = 3x + 5 will be a value of x for which p(x) becomes 0.
Equating p(x) to 0, we get the following equation:
3x + 5 = 0
Subtracting 5 from both sides of the equation, we get:
3x = -5
Dividing by 3, to get the value of x, we get:
 $x=-\dfrac{5}{3}$ , which is the zero of the given polynomial.
Check: Substituting the value $x=-\frac{5}{3}$ in p(x) = 3x + 5, we get:
 $p\left( \dfrac{-5}{3} \right)=3\times \left( \dfrac{-5}{3} \right)+5=-5+5=0$ , hence $x=-\dfrac{5}{3}$ is the zero of p(x).
The zero of a polynomial, is also the point on its graph where it touches/cuts the x-axis (y=0). The graph of p(x) = 3x + 5 is shown below:

The correct answer option is D. $-\dfrac{5}{3}$.

Note:
The degree of a polynomial/equation is the highest power of the variables occurring in it.
(xy) has a degree of two, because the variables x and y are multiplied together.
The graph of a linear polynomial (degree 1) is a straight line.