Question

Find all zeroes of polynomial 2x4+7x3-19x2-14x + 30, if two zeroes are root 2 and - root 2. find other two zeroes.

Answer 1

Here is your answer......

Answer 2

Answer:

The other zeroes of the given polynomial are -5 and 3/2

Step-by-step explanation:

Since , two zeroes are √2 and -√2 .

Therefore, (x-√2)(x+√2)=x²-(√2 )²

= x²-2 is a factor of the given polynomial.

Now , we apply the division algorithm to the given polynomial and x²-2.

quotient:2x²+7x-15_______

x²-2)2x⁴+7x³-19x²-14x+30(

*****2x⁴+0-4x²

______________________

********7x³-15x²-14x

********7x³+ 0 -14x

_____________________

***********-15x²+30

********** -15x²+30

_______________________

Remainder ( 0 )

So,

2x⁴+7x³-19x²-14x+30 =(x²-2)(2x²+7x-15)

Now,

2x²+7x-15

Splitting the middle term, we get

= 2x²+10x-3x-15

= 2x(x+5)-3(x+5)

= (x+5)(2x-3)

So, it's zeroes are x=-5 and x =3/2

Therefore,

The other zeroes of the given polynomial are -5 and 3/2

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