Question

If alpha and beta are the roots of the quadratic equation 4x^2 + 3x +7=0, then 1/alpha+1/beta=

Answer 1

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

Answer 2

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