Question

If root 5 and minus root 5 are two zeroes of the polynomial x3+3x2-5x-15 find the third zero

Answer 1

Answer:

here is an easy method

Step-by-step explanation:

∝=√5  ,  β= -√5

we know ∝+β+y= -b/a

⇒ √5 + -√5 + y = -3/1

⇒ therefore y = -3

Answer 2

Answer:

The third zero is (-3)

Step-by-step explanation:

Given,If √5 and (-√5)are two zeroes of the polynomial

${x}^{3} + 3 {x}^{2} - 5x - 15$

Let another zero be y.

Then we can write

$(x - \sqrt{5} )(x + \sqrt{5})(x - y) ={x}^{3} + 3 {x}^{2} - 5x - 15$

$( {x}^{2} - { \sqrt{5} }^{2} )(x - y) = {x}^{3} + 3 {x}^{2} - 5x - 15$

$( {x}^{2} - 5)(x - y) = {x}^{3} + 3 {x}^{2} - 5x - 15$

${x}^{3} - y {x}^{2} - 5x + 5y = {x}^{3} + 3 {x}^{2} - 5x - 15$

We are comparing both side and get

$- y = 3....(1)$

and

$5y = - 15.....(2)$

From equation (1),

$- y = 3 \\ y = - 3$

and from equation (2),

$5y = - 15 \\ y = - \frac{15}{5} \\ y = - 3$

So we can say $y = - 3$

Therefore third zero is (-3).

Here applied formula

${a}^{2} - {b}^{2} = (a + b)(a - b)$

More concept about zeroes of Polynomial

1.https://brainly.in/question/13360443?utm_source=android&utm_medium=share&utm_campaign=question

2.https://brainly.in/question/18596686?utm_source=android&utm_medium=share&utm_campaign=question