Question

find the other zeroes of the polynomial x^4-7x2+12 if it is given that two of its zeros are √3 and -√3​

Answer 1

Answer:

Another zeros are √4 and -√4

Explanation:

Given polynomial,

⇒ p(x) = x⁴ - 7x² + 12

Whose two of it's zeros are √3 and -√3

We need to find the other two zeros.

Here, if √3 and -√3 are zeros of p(x) then, we can say that, (x + √3)(x - √3) is a factor of p(x)

Or,

= (x + √3)(x - √3)

= x² - 3 is a factor of p(x)

On dividing p(x) by its factor we get the quotient as another factor.

By long divison method,

x² - 3)x⁴ - 7x² + 12(x² - 4

-

x⁴ - 3x²

- 4x² + 12

-

-4x² + 12

0

We get another factor as x² - 4

On factorising,

⇒ x² - 4 = 0

⇒ x² = 4

⇒ x = ±√4

Hence, the another zeros are √4 and -√4