Question

if alpha and beta are zeroes of x^2+7x+12 then find value of 1/alpha+ 1/beta +2alpha beta

Answer 1

Heya !!

Here's your answer..⤵
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p(x) = x² + 7x + 12

a = 1
b = 7
c = 12

Sum of zeros = -b/a

α + β = -7

Product of zeros = c/a

αβ = 12

$= \frac{1}{ \alpha } + \frac{1}{ \beta } + 2( \alpha \beta ) \\ \\ = \frac{ \alpha + \beta }{ \alpha \beta } + 2(12) \\ \\ = \frac{ - 7}{12} + 24 \\ \\ = \frac{ - 7 + 288}{12} \\ \\ = \frac{281}{12} \\ \\ = 23.41$
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Hope it helps..
Thanks

Answer 2

Answer:

x² + 7x +12

Alpha + beta = -7

Alpha * beta = 12

I/alpha +1/beta =(al + bet)/all*bet

= -7/12

And 2al.bet = 24

-7/12- 24

= -283/12