If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other,
then it
(a) has no linear term and the constant term is negative.
(b) has no linear term and the constant term is positive.
(c) can have a linear term but the constant term is negative.
(d) can have a linear term but the constant term is positiv
Answers
Answer:
a
Step-by-step explanation:
One root is negative of the other
So, sum of roots is zero
So, linear term does not exist
Product of roots is negative
So, constant term is negative
Answer is option a
Step-by-step explanation:
Given:-
One of the zeroes of a quadratic polynomial of the form x^2+ ax + b is the negative of the other.
To find:-
Check whether it has one of the following?
(a) has no linear term and the constant term is negative.
(b) has no linear term and the constant term is positive.
(c) can have a linear term but the constant term is negative.
(d) can have a linear term but the constant term is positive
Solution:-
Given that
One of the zeroes of a quadratic polynomial of the form x^2+ ax + b is the negative of the other.
Let other zero be A
Then, the other zero = -A
We know that
The Quadratic Polynomial whose zeroes α and β is K[x^2-(α+ β)x+α β]
=> K[x^2-(A-A)x+(A)(-A)]
=> K[x^2-0X-A^2]
=> K[x^2-A^2]
If K = 1 ,then the required Polynomial is x^2-A^2.
On comparing this with x^2+ ax + b then a= 0 and b= -A^2
So ,Linear term is zero and constant term is negative.
It has x^2 term and constant term and constant term is negative.
Answer:-
If one zero of a quadratic polynomial is negative to the other then the quadratic polynomial has no linear term but the constant term is negative.
Option A
Used formulae:-
The Quadratic Polynomial whose zeroes α and β is K[x^2-(α+ β)x+α β]