Question

alfa beta are 2 zeros of quadratic eq. x^2-5x+6 find the value of 1/alfa and 1/ beta

Answer 1

★ QUADRATIC RESOLUTION ★

Given function :

x² - 5x + 6 = 0

having , α and β as it's roots ,

There's a mistake in question , it's 1/ alpha + 1/ beta ...

Hence ,

1/ α + 1/ β

α + β / αβ

Unlike , other methods ,

Generating the roots because it's real roots are available and can be easily obtained -

x² - 5x + 6 = 0

x² - 2x - 3x + 6 = 0

x ( x - 2 ) - 3 ( x - 2 ) = 0

x - 3 ( x - 2 ) = 0

x = 3, 2

Hence , required result is

3 + 2 / 3 ( 2 )

5 / 6

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Answer 2

Hi ,

Here I am using p, and q are zeroes

instead of alfa and beta

Compare x² - 5x + 6 = 0 with

ax² + bx +c = 0 ,

a = 1 , b = - 5 , c = 6

Sum of the zeroes = - b/a

p + q = - ( -5 ) / 1 = 5 ---- ( 1 )

Product of the roots = c/a

pq = 6/1 = 6 -----( 1 )

Now ,

1/p + 1/q = ( q + p ) / pq

= 5/6

I hope this helps you.

:)