Question

if x-root2 is a factor of cubic polynomial =x^3-root 2x^2-4x+4root2 find remaining zeroes of polynomial ​

Answer 1

Answer:

Step-by-step explanation:

✓2 is the factor of the given polynomial

(X-✓2) is the factor of the polynomial$6X³+✓2X²-10X-4✓2$

Divide the polynomial $6X³-✓2X-10X-4✓2$by X-✓2. Then we get,

Quotient = $6X²+7✓2X+4$

Factories the Quotient ,

$6X²+7✓2X+4$

$6X²+4✓2X+3✓2X + 4$

$2X(3X + 2✓2) + ✓2(3X+2✓2)$

$(3X+2✓2) ( 2X+✓2)$

$3X = -2✓2. OR 2X = -✓2$

$X = -2✓2/3. OR X = -✓2/2$

Hence,

$-2✓2/3 and -✓2/2$ are the two other ZEROS of the polynomial

hope it helps

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