Question

please answer the question

Answer 1

Hii friend,

The given polynomial is F(X) = 2X⁴-2X³-7X²+3X+6

Since,-✓3/2 and ✓3/2 are the zeros of F(X) , it follows that each one of (X+✓3/2) and (X-✓3/2) is a factor of F(X).

Therefore,

(X+✓3/✓2) (X-✓3/✓2) = (X²-3/2) = (2X²-3/2) is a factor of F(X).

Consequently , (2X²-3) is a factor of F(X).

On dividing F(X) by (2X²-3), we get

2X²-3)2X⁴-2X³-7X²+3X+6(X²-X-2

+ 2X⁴ -3X²
- +
__________________
0 - 2X³-4X² +3X+6
- 2X³ +3X
+ -
__________________
0 - 4X² +0 +6
-4X² +6
+ -
___________________

We get,

REMAINDER = 0

And ,

Quotient = X²-X-2

Factories the Quotient then we will get the two other zeros of the F(X)

=> X²-X-2

=> X²-2X+X-2

=> X(X-2) +1(X-2)

=> (X-2) = 0. OR (X+1) = 0

=> X = 2. OR X = -1

Hence,

✓3/2 , -✓3/2 , 2 and -1 are the four zeros of the polynomial 2X⁴-2X³-7X²+3X+6.

HOPE IT WILL HELP YOU..... :-)
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