Question

If α and β are the zeros of the quadratic polynomial f(x) = x

2 + 3x + 2,

find the value of 1/α + 1/β – 2αβ.​

Answer 1

f( x ) = x² +3x + 2

Given α and β are zeroes of polynomial

x² + 3x + 2 = 0

x² + x + 2x + 2 = 0

x ( x + 1 ) + 2 ( x + 1 ) = 0

( x + 1 ) ( x + 2 ) = 0

Hence α = – 1, β = – 2

1/α + 1/β – 2αβ

= ( 1/–1 ) + ( 1 / – 2 ) – [ 2 ( – 1) ( – 2) ]

= – 1 – 1/2 – 4

= – 5 – 1/2

= – 11/2

– 11/2 is the answer

Answer 2

Answer:

$\frac{-11}{2}$ or $-5.5$

Step-by-step explanation:

Let $\alpha, \beta$ be the zeroes of the polynomial $P(x)=x^2+3x+2$

Using Relations between roots and coefficients of a quadratic polynomial, we get -

$\alpha+\beta=\dfrac{-3}{1}=-3$            .................(1)

$\alpha\beta=\dfrac{2}{1}=2$             .................(2)

Now,

$\dfrac{1}{\alpha}+\dfrac{1}{\beta}-2\alpha\beta$

$=> \dfrac{\beta+\alpha}{\alpha\beta}-2\alpha\beta$

$=> \dfrac{-3}{2}-2\times 2$           [from(1 and (2)]

$=> \dfrac{-3}{2}-4$

$=> \dfrac{-3-8}{2}$

$=> \dfrac{-11}{2}$

$=> -5.5$