Question

Statement P : If α, β, γ are the zeroes of the cubic

polynomial ax3

+ bx2

+ cx + d then αβγ =

c

a

Statement Q : r(z) = z3 has only one zero

A) Statement P is true, q is false

B) P is false and Q is false

C) P is true and Q is true

D) P is false and Q is true​

Answer 1

Step-by-step explanation:

Given:-

Statement P : If α, β, γ are the zeroes of the cubic

polynomial ax^3+ bx^2+ cx + d then αβγ = c/a

Statement Q : r(z) = z3 has only one zero

To find:-

A) Statement P is true, q is false

B) P is false and Q is false

C) P is true and Q is true

D) P is false and Q is true

Solution:-

Statement P : If α, β, γ are the zeroes of the cubic

polynomial ax^3+ bx^2+ cx + d then αβγ = c/a

This is false statement.

Reason:-

The product of the zeroes αβγ = -d/a

Statement Q : r(z) = z^3 has only one zero

This is false statement.

Reason:-

Given cubic polynomial r(z) = z^3

Since it is a cubic Polynomial then it has at most three zeroes

r(z) = z^3 = 0

=>z = 0

The zeroes of r(z)=z^3 are 0,0,0

Answer:-

Both The statements P and Q are False statements

Option B

Used formulae:-

• The standard cubic Polynomial is ax^3+bx^2+cx+d
• A cubic Polynomial has at most three zeroes.

If α, β, γ are the zeroes then,

• Sum of the zeroes = -b/a
• Sum of the product of the two zeroes taken at a time = c/a
• Product of th zeroes = -d/a