Question

find all the zeroes of polynomial 2x^4 + x^3 - 14x^2 + 5x +6 if two of the zeroes are -3 and 1​

Answer 1

$\huge{ \underline{ \underline{ \sf{ \blue{Detailed \: \: Answer}}}}}$

• To Find : All the zeroes of polynomial 2x⁴ + x³ - 14x² + 5x + 6

• Given : Two of it's zeroes are -3 & 1

The given polynomial is 2x⁴ + x³ - 14x² + 5x + 6.

Let us take -3 & 1.

x + 3 = 0 ; x - 1 = 0

➛ ( x + 3 ) ( x - 1 )

Simplifying these,

➛ x² - x + 3x - 3

➛ x² + 2x - 3

We have to divide the given polynomial with x² + 2x - 3.

Have a look at the attachment for the long division.

After the long division,

We get a quotient which is 2x² - 3x - 2.

Splitting the middle term for this equation we get,

➛ 2x² - 4x + x - 2

➛ 2x ( x - 2 ) + 1 ( x - 2 )

➛ ( x - 2 ) ( 2x + 1 )

➛ ‍ x = 2 ; x = $\frac{-1}{2}$

Hence, these are the zeroes of the polynomial.

You can substitute the values and verify the answer!