Question

If alpha abd beta are the zeros of x square + 3x +4 , the value of 1/alpha +1/beta - 2alpha beta

Answer 1

α and β are the two zeroes of the polynomial x² + 3x + 4 = 0 .

★ Sum of zeroes:

α + β = - coefficient of x / coefficient of x²

⇒ α + β = -3

★ Product of the zeroes:

αβ = constant term / coefficient of x²

⇒ αβ = 4

Now,

1/α + 1/β - 2αβ [ Given ]

⇒ β + α / αβ - 2αβ

⇒ α + β / αβ - 2αβ

Substituting the values

⇒ -3/4 - 2 × 4

⇒ -3/4 - 8

⇒ -3 - 32 / 4

⇒ -35 / 4

Answer 2

$\huge\mathfrak{Answer:}$

Given:

• We have been given that α and β are the two zeroes of the polynomial x² + 3x + 4 = 0.

To Find:

• We need to find the value of 1/α + 1/β - 2αβ.

Solution:

The given polynomial is p(x) = x² + 3x + 4 = 0.

It is given that α and β are the two zeroes of this polynomial.

a = 1, b = 3 and c = 4

Sum of zeroes (α + β)

= -b/a

= -3/1_____(1)

Product of zeroes (αβ)

= c/a

= 4/1______(2)

Now, we need to find the value of 1/α + 1/β - 2αβ.

=> (β + α)/αβ - 2αβ

=> (α + β)/αβ - 2αβ

Substituting the values from equation 1 and 2, we have

⇒ (-3/1)/4 - (2 × 4)

=> -3/4 - 8

Taking LCM as 4,

=> -3/4 - 8/1 × 4/4

=> -3/4 - 32/4

=> (-3 - 32)/4

=> -35/4

Hence, the value of 1/α + 1/β - 2αβ is -35/4.