If alpha and beta are the roots of the quadratic equation 4x^2 + 3x +7=0, then 1/alpha+1/beta=
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α and β are the two zeroes of the quadratic polynomial 4x² + 3x + 7 = 0 .
★ Sum of zeroes:
α + β = - coefficient of x / coefficient of x²
⇒ α + β = -3/4 .......( 1 )
★ Product of the zeroes:
αβ = constant term / coefficient of x²
⇒ αβ = 7/4 .....( 2 )
Now,
1/α + 1/β [ Given ]
⇒ β + α / αβ
⇒α + β / αβ
Substituting the values
⇒ -3/4 / 7/4 [ From ( 1 ) & ( 2 ) ]
⇒ -3/4 × 7/4
⇒ -3/7
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ANSWER:
Given , α & β are the roots of quadratic polynomial 4x² + 3x + 7 = 0
We need to find , 1/α + 1/β
Finding 1/α + 1/β using α + β = -b/a & αβ = c/a
Where
- b : coefficient of x = 3
- a : coefficient of x² = 4
- c : constant term = 7
1/α + 1/β
→ α + β/αβ
→ - b/a/c/a
→ - b/c
→ - 3/7 ( Answer )
.°. Hence, 1/α + 1/β = -3/7
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