Question

(d) Determine all the zeros of
X4 - X3 - 8x2 +2x + 12
if two of its zeros are √2 and-√2​

Answer 1

x

2

−x−6=0

⇒x

2

−3x+2x−6=0

⇒x(x−3)+2(x−3)=0

⇒(x−3)(x+2)=0

⇒x=−2,3

Hence, all the zeros are −2,3,

2

,−

2

HOPE IT'S HELPFUL TO YOU

Answer 2

$\huge\fcolorbox{red}{yellow}{ANSWER}$

Let, p(x)=x

4

−x

3

−8x

2

+2x+12

Since,

2

and −

2

are zeros of p(x)

⇒(x−

2

) and (x+

2

) divides p(x) (∵Factor thm.)

⇒(x−

2

)(x+

2

) divides p(x)

⇒(x

2

−2) divides p(x)

x

2

−2)

x

4

−x

3

−8x

2

+2x+12

( x

2

−x−6

−

x

4

+

−

2x

2

−x

3

−6x

2

+2x+12

+

−

x

3

−

+

2x

−6x

2

+12

+

−

6x

2

−

+

12

0

Now, the other zeros can be obtained from on solving x

2

−x−6=0

⇒x

2

−3x+2x−6=0

⇒x(x−3)+2(x−3)=0

⇒(x−3)(x+2)=0

⇒x=−2,3

Hence, all the zeros are −2,3,

2

,−

2