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# HELP QUICK!

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One of the roots of 2x^3-9x^2+13x+k=0 is x=2.Find the other 2 roots. Explain how you got the answer.

Feb 17, 2021

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One of the roots of 2x^3-9x^2+13x+k=0 is $$x_1=2$$.Find the other 2 roots. Explain how you got the answer.

Hello whatdoiputhere!

$$(2x ^ 3-9x ^ 2 + 13x + k)$$  $$:(x-2)=$$  $$2x^2-5x+3$$

$$\underline{2x^3-4x^2}$$

$$-5x^2+13x$$

$$\underline{-5x^2+10x}$$

$$3x+k$$

$$\underline{3x-6}$$

$$0$$

$$k=-6$$

$$2x^2-5x+3=0\\ x^2-2.5x+1.5=0\\ x=1.25\pm \sqrt{1.25^2-1.5}\\ \color{blue}x=1.25\pm0.25$$

$$x\in\{1,1.5,2\}$$

!

Feb 17, 2021
edited by asinus  Feb 17, 2021

#1
+11656
+5

One of the roots of 2x^3-9x^2+13x+k=0 is $$x_1=2$$.Find the other 2 roots. Explain how you got the answer.

Hello whatdoiputhere!

$$(2x ^ 3-9x ^ 2 + 13x + k)$$  $$:(x-2)=$$  $$2x^2-5x+3$$

$$\underline{2x^3-4x^2}$$

$$-5x^2+13x$$

$$\underline{-5x^2+10x}$$

$$3x+k$$

$$\underline{3x-6}$$

$$0$$

$$k=-6$$

$$2x^2-5x+3=0\\ x^2-2.5x+1.5=0\\ x=1.25\pm \sqrt{1.25^2-1.5}\\ \color{blue}x=1.25\pm0.25$$

$$x\in\{1,1.5,2\}$$

!

asinus Feb 17, 2021
edited by asinus  Feb 17, 2021