Advertisement Remove all ads

If √ 5 and − √ 5 Are Two Zeroes of the Polynomial X3 + 3x2 − 5x − 15, Then Its Third Zero is - Mathematics

MCQ

If \[\sqrt{5}\ \text{and} - \sqrt{5}\]   are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is

Options

  •  3

  • -3

  • 5

  • -5

Advertisement Remove all ads

Solution

Let `alpha =sqrt5 `  and `beta -sqrt5` be the given zeros and  y be the third zero of the polynomial `x^3 + 3x^2 - 5x -15`. Then,

By using `alpha + beta + y  (-text{coefficient of }x^2)/(text{coefficient of } x^3)`

`alpha + beta + y = -3 /1`

`alpha + beta + y = -3`

Substituting `alpha = sqrt5`  and `beta = -sqrt5` in `alpha + beta  + y = -3`

We get

`sqrt5 - sqrt5 + y = -3`

`cancel(sqrt5) - cancel(sqrt5) + y = -3`

` y =-3`

Hence, the correct choice is `(b).`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 28 | Page 64
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×