How do you find all zeros of the function $f (x) = 3 x^{2} - 17 x + 20$ $f(x)=3x^2-17x+20$ ?

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How do you find all zeros of the function $f (x) = 3 x^{2} - 17 x + 20$ $f(x)=3x^2-17x+20$ ?

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Answer 1 · 2016-03-12T00:11:20

Use the quadratic formula to find:

$x = 4$ $x = 4$ or $x = \frac{5}{3}$ $x = 5/3$

Explanation:

$3 x^{2} - 17 x + 20$ $3x^2-17x+20$ is of the form $a x^{2} + b x + c$ $ax^2+bx+c$ with $a = 3$ $a=3$ , $b = - 17$ $b=-17$ and $c = 20$ $c=20$ .

This has zeros given by the quadratic formula:

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

$= \frac{17 \pm \sqrt{{(- 17)}^{2} - (4 \cdot 3 \cdot 20)}}{2 \cdot 3}$ $=(17+-sqrt((-17)^2-(4*3*20)))/(2*3)$

$= \frac{17 \pm \sqrt{289 - 240}}{6}$ $=(17+-sqrt(289-240))/6$

$= \frac{17 \pm \sqrt{49}}{6}$ $=(17+-sqrt(49))/6$

$= \frac{17 \pm 7}{6}$ $=(17+-7)/6$

That is $x = 4$ $x = 4$ or $x = \frac{5}{3}$ $x = 5/3$

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How do you find all zeros of the function $f (x) = 3 x^{2} - 17 x + 20$ $f(x)=3x^2-17x+20$ ?

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Explanation:

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