Question

Obtain all the other zeroes of
2^4 − 5^3 − 13^2 + 25 + 15, if two of its zeroes are −√5 and √5 .​​

Answer 1

Step-by-step explanation:

Two zeroes are

3

5

and −

3

5

So we can write it as, x =

3

5

and x = −

3

5

we get x−

3

5

=0 and x+

3

5

=0

Multiply both the factors we get,

x

2

−

3

5

=0

Multiply by 3 we get

3x

2

−5=0 is the factor of 3x

4

+6x

3

−2x

2

−10x−5

Now divide, 3x

4

+6x

3

−2x

2

−10x−5 by 3x

2

−5=0 we get,

Quotient is x

2

+2x+1=0

Compare the equation with quadratic formula,

x

2

−(Sum of root)x+(Product of root)=0

⇒Sum of root =2

⇒Product of the root =1

So, we get

⇒x

2

+x+x+1=0

⇒x(x+1)+1(x+1)=0

⇒x+1=0,x+1=0

⇒x=−1,x=−1

So, our zeroes are −1,−1,

3

5

and −

3

5