# 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

•  3

• -3

• 5

• -5

#### 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).

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 28 | Page 64