If α and β are the zeroes of a quadratic polynomial such that α β + = 0 and α β − = 8. Find the quadratic polynomial having α and β as its zeroes.
Please answer it fast, it's urgent.
I will follow the one who will answer the question.
Share
If α and β are the zeroes of a quadratic polynomial such that α β + = 0 and α β − = 8. Find the quadratic polynomial having α and β as its zeroes.
Please answer it fast, it's urgent.
I will follow the one who will answer the question.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
The quadratic polynomial is equal to - 8.
Step-by-step explanation:
Given,
α + β = 0 and αβ = - 8
To find, the quadratic polynomial = ?
If α and β be the roots of quadratic polynomial.
The quadratic polynomial:
- (α + β)x + αβ
= - (0)x + (- 8)
= - (0)x - 8
= - 8
∴ The quadratic polynomial = - 8
Thus, the quadratic polynomial is equal to - 8.
Verified answer
Therefore the quadratic polynomial is f(x) =k(x²-16) [where k is a constant]
Step-by-step explanation:
Polynomial: A polynomial makes with variables and coefficients.
Quadratic Polynomial: A quadratic polynomial is function of one variable and the degree of the variable is 2.
Given that,
α+ β= 0......(1)
α- β= 8.....(2)
____________
2α=8
⇒α=4
Then putting α=4 in equation (1)
4+β=0
⇒β= -4
If a and b are two zeros of quadratic polynomial, then the quadratic polynomial is f(x)=(x-a)(x-b)
Therefore the quadratic polynomial is
f(x)=k(x-4)[x-(-4)] [where k is a constant]
=k(x-4)(x+4)
=k(x²-4²)
=k(x²-16)