Q. 244.5( 17 Votes )

# Find all the zero

Answer :

Let us assume f (x) = x4 + x3 ‒ 23x2 ‒ 3x + 60

As √3 and –√3 are the zeros of the given polynomial therefore each one of (x - √3) and (x - √3) is a factor of f (x)

Consequently, (x – √3) (x + √3) = (x2 – 3) is a factor of f(x)

Now, on dividing f (x) by (x2 – 3) we get: f (x) = 0

(x2 + x – 20) (x2 – 3) = 0

(x2 + 5x – 4x – 20) (x2 – 3)

[x (x + 5) – 4 (x + 5)] (x2 – 3)

(x – 4) (x + 5) (x – ) (x + ) = 0

x = 4 or x = - 5 or x = or x = - Hence, all the zeros of the given polynomial are , - , 4 and - 5

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