Question

3x²+8x+2=0
$(\frac{1}{ \alpha } + \frac{1}{ \beta } )$


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Answer 1

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