3x²+8x+2=0

Answers
Given:-
- 3x² + 8x + 2 = 0
- α and β are roots of this polynomial
To find:-
- 1/α + 1/ β
Answer:-
We know the relation between zeroes and coefficients of a quadratic polynomial.
If the roots of p(x) = ax² + bx + c are α and β, then,
▪ α + β = -b/a
▪ αβ = c/a
We have to use this relation here.
Here, given polynomial is 3x² + 8x + 2 and on comparing it with the general form, ax² + bx + c, we get,
- a = 3
- b = 8
- c = 2
So,
▪α + β = -b/a = -8/3 ----( 1 )
▪αβ = c/a = 2/3 ----( 2 )
Dividing equation ( 1 ) by equation ( 2 ):-
(α + β) / (αβ) = [(-8/3) / (2/3)]
→ (α/αβ) + (β/αβ) = -8/3 × 3/2
→ 1/β + 1/α = -4
→ 1/α + 1/β = -4 Ans.
Other relations:-
The relation between zeroes and
coefficients of a cubic polynomial:-
If the roots of p(x) = ax³ + bx² + cx + d are α, β and γ then,
▪ α + β + γ = -b/a
▪ αβ + βγ + γα = c/a
▪ αβγ = -d/a