Question

Question 11. Find other zeroes of the polynomial x - 7x7+ 12 if it is given that two of its zeroes are V3 and -V3.5​

Answer 1

Answer:

follow me

Explanation:

Since the two zeroes of the given polynomial p(x)=2x

4

+7x

3

−19x

2

−14x+30 are

2

and −

2

, therefore,

(x−

2

)(x+

2

)=x

2

−2 is a factor of the given polynomial.

now, we divide the polynomial p(x)=2x

4

+7x

3

−19x

2

−14x+30 by x

2

−2 as shown below:

Therefore, 2x

4

+7x

3

−19x

2

−14x+30=(x

2

−2)(2x

2

+7x−15)

Now, we factorize 2x

2

+7x−15 as follows:

2x

2

+7x−15=0

⇒2x

2

+10x−3x−15=0

⇒2x(x+5)−3(x+5)=0

⇒(2x−3)(x+5)=0

⇒2x−3=0,x+5=0

⇒2x=3,x=−5

⇒x=

2

3

,x=−5

Hence, the zeroes of the polynomial p(x)=2x

4

+7x

3

−19x

2

−14x+30 are

2

,−

2

,

2

3

,−5.