Question

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √5/3 and –√5/3​

Answer 1

Answer:

other two zeros are -1 and -1

Explanation:

Given polynomial,

⇒ p(x) = 3x⁴ + 6x³ - 2x² - 10x - 5

Whose two of it's zeros are √5/3 and -√5/3

Then,

= (x + √5/3)(x - √5/3) is a factor of p(x)

Solving further,

= (x² - 5/3)

Dividing p(x) by its factor :-

3x² + 6x + 3

x² - 5/3)3x⁴ + 6x³ - 2x² - 10x - 5(

3x⁴ - 5x²

(-) (+)

6x³ + 3x² - 10x - 5

6x³ - 10x

(-) (+)

3x² - 5

3x² - 5

(-) (+)

0

We got another factor as 3x² + 6x + 3

On factorising,

= 3x² + 6x + 3

= 3x² + 3x + 3x + 3

= 3x(x + 1) + 3(x + 1)

= (x + 1)(3x + 3)

Then,

⇒ x + 1 = 0

⇒ x = -1

And also,

⇒ 3x + 3 = 0

⇒ 3x = -3

⇒ x = -3/3

⇒ x = -1

∴ -1 and -1 are the other two zeros of p(x)