Question

If the polynomial p(x)=3x^4+3x^3-11x^2-5x+10 is completely divisible by 3x^2-5 find all its zeros

Answer 1

hope this helps you guys

Answer 2

Answer:

$All \:zeroes \: of \: p(x),\\are \: -\frac{\sqrt{5}}{\sqrt{3}},</p><p>\frac{\sqrt{5}}{\sqrt{3}},2\:and\: -1$

Step-by-step explanation:

Given polynomial :

p(x)=3x⁴+3x³-11x²-5x+10

is completely divisible by 3x²-5 .

quotient : x²+x-2

3x²-5)3x⁴+3x³-11x²-5x+10(x²

****** 3x⁴+0-5x²

________________________

********* 3x³-6x²-5x

********* 3x³+0 -5x

________________________

*********** -6x²+10

*********** -6x²+10

________________________

Remainder (0)

Now,

p(x)=(3x²-5)(x²-x-2)

= (3x²-5)(x²-2x+1x-2)

= [(√3x)²-(√5)²[x(x-2)+1(x-2)]

=(√3x+√5)(√3x-√5)(x-2)(x+1)

Therefore,

$All \:zeroes \: of \: p(x),\\are \: -\frac{\sqrt{5}}{\sqrt{3}},</p><p>\frac{\sqrt{5}}{\sqrt{3}},2\:and\: -1$

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