3 years ago

Find the value of x. A. 60 B. 40 C. 30 D. 50

Mathematics

2 answers:

scZoUnD [109]3 years ago

6 0

the answer to the question is choice A

AVprozaik [17]3 years ago

4 0

Do you have the equation needed to solve for x?

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Read 2 more answers

Find the polynomial f(x) of degree 3 with real coefficients that has a y-intercept of 60 and zeros 3 and 1+3i.

Sauron [17]

$\bf \begin{cases} x=3\implies &x-3=0\\ x=1+3i\implies &x-1-3i=0\\ x=1-3i\implies &x-1+3i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x-3)(x-1-3i)(x-1+3i)=0 \\\\\\ (x-3)\underset{\textit{difference of squares}}{([x-1]-3i)([x-1]+3i)}=0\implies (x-3)([x-1]^2-[3i]^2)=0 \\\\\\ (x-3)([x^2-2x+1]-[3^2i^2])=0\implies (x-3)([x^2-2x+1]-[9(-1)])=0$

[ correction added, Thanks to @stef68 ]

$\bf (x-3)([x^2-2x+1]+9)=0\implies (x-3)(x^2-2x+10)=0 \\\\\\ x^3-2x^2+10x-3x^2+6x-30=0\implies x^3-5x^2+16x-30=f(x) \\\\\\ \stackrel{\textit{applying a translation with a -2f(x)}}{-2(x^3-5x^2+16x-30)=f(x)}\implies -2x^3+10x^2-32x+60=f(x)$

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4 years ago