What are all the possible rational zeros for $f (x) = 3 x^{2} + 2 x - 1$ $f(x)=3x^2+2x-1$ ?

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What are all the possible rational zeros for $f (x) = 3 x^{2} + 2 x - 1$ $f(x)=3x^2+2x-1$ ?

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Answer 1 · 2017-03-18T07:12:22

Zeros are $\frac{1}{3}$ $1/3$ and $- 1$ $-1$

Explanation:

Observe that in quadratic function $f (x) = 3 x^{2} + 2 x - 1$ $f(x)=3x^2+2x-1$ , the discriminant $b^{2} - 4 a c = 2^{2} - 4 \times 3 \times (- 1) = 16$ $b^2-4ac=2^2-4xx3xx(-1)=16$ is a perfect square and hence, we can factorize it with rational factors,

$f (x) = 3 x^{2} + 2 x - 1$ $f(x)=3x^2+2x-1$

= $3 x^{2} + 3 x - x - 1$ $3x^2+3x-x-1$

= $3 x (x + 1) - 1 (x + 1)$ $3x(x+1)-1(x+1)$

= $(3 x - 1) (x + 1)$ $(3x-1)(x+1)$

Hence, zeros are given by $3 x - 1 = 0$ $3x-1=0$ and $x + 1 = 0$ $x+1=0$

i.e. they are $\frac{1}{3}$ $1/3$ and $- 1$ $-1$

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What are all the possible rational zeros for $f (x) = 3 x^{2} + 2 x - 1$ $f(x)=3x^2+2x-1$ ?

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Explanation:

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What are all the possible rational zeros for f(x)=3x^2+2x-1f(x)=3x2+2x−1f(x)=3x^2+2x-1?

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What are all the possible rational zeros for $f (x) = 3 x^{2} + 2 x - 1$ $f(x)=3x^2+2x-1$ ?