1 thought on “<br />
Find a quadratic polynomial, the sum and product of whose zeros are -1/3 and 4.<br /><br />”
Given:–
Sum of zeroes = -1/3
Product of zeroes = 4
To find:–
Quadratic polynomial = ?
Solution:–
When we know the sum and product of zeroes and when we are supposed to find the quadratic polynomial, we use the below mentioned formula.
Quadratic polynomial=x²–(α +β)x +αβ
Where
(α + β) is the sum of zeroes
αβ is the product of zeroes
Quadratic polynomial = x² – (α + β)x + αβ
➝ Quadratic polynomial = x² – (-1/3)x + 4
⇒ Quadratic polynomial = x² + 1/3x + 4
Here we Multiply 3 throughout the polynomial to eleminate the fraction.
➥ Quadratic polynomial = 3x² + x + 12
KNOW MORE:
α and β are the general zeroes of all polynomials because when the given equation is factorised, the factors are got. When these factors are equated to zero we get the value of α and β.
Given :–
To find :–
Quadratic polynomial = ?
Solution :–
When we know the sum and product of zeroes and when we are supposed to find the quadratic polynomial, we use the below mentioned formula.
Quadratic polynomial = x² – (α + β)x + αβ
Where
Quadratic polynomial = x² – (α + β)x + αβ
➝ Quadratic polynomial = x² – (-1/3)x + 4
⇒ Quadratic polynomial = x² + 1/3x + 4
Here we Multiply 3 throughout the polynomial to eleminate the fraction.
➥ Quadratic polynomial = 3x² + x + 12
KNOW MORE:
α and β are the general zeroes of all polynomials because when the given equation is factorised, the factors are got. When these factors are equated to zero we get the value of α and β.