Question

if alpha and beta are the zeros of quadratic polynomial f(x)=ax² + bx + c, then evaluate,
$1 \div \alpha + 1 \div \beta - 2 \alpha \beta$
​

Answer 1

Given :

• α and β are the zeroes of the quadratic polynomial f ( x ) = ax² + bx + c

To Find :

• 1/α + 1/β - 2αβ

Solution :

➨ 1/α + 1/β - 2αβ

Solve 1/α + 1/β by taking LCM

➨ ( β + α )/αβ - 2αβ

we know that

➨ α + β = - b/a

➨ αβ = c/a

so

➨ ( - b/a ) / c/a - 2c/a

➨ - b/c - 2c/a

➨ - [ b/c + 2c/a ]

Answer 2

heya ❤️

Hello friend your answer is

α and β are the zeros then Ax²+Bx+C

α-β find..

Sum of zeroes = α+β

-b/a=

-B/A

Product of zeroes =c/a

C/A

now α-β=(α-β)²=(α+β)²-4αβ

use this identity

=-B/A-4C/A

-B/A-4C/A

-B-4C/A

α-β=√-B-4C/A

I hope it helps