Question

Find a zero of the polynomial p(x) = 2x + 1.​

Answer 1

Step-by-step explanation:

p(x) = 0

2x + 1 = 0

2x = 1

x = 1

2

Answer 2

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Finding a zero of p(x), is the same as solving the equation p(x) = 0

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Now,

$2x\:+\:1\:=\:0\:gives \:us\:x\:=\:-\frac{1}{2}$

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So, $-\frac{1}{2}$ is a zero of the polynomial 2x + 1.

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Now, if p(x) = ax + b, a ≠ 0, is a linear polynomial, how can we find a zero of p(x)?

Finding a zero of the polynomial p(x), amount to solving the polynomial equation p(x) = 0.

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Now, p(x) = 0 means

ax + b = 0, a ≠ 0

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So, ax = -b

x = $-\frac{b}{a}$.

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So, x = $-\frac{b}{a}$ is the only zero of p (x), i.e., a linear polynomial has one and only one zero.

Now we can say that 1 is the zero of x -1, and -2 is the zero of x + 2.