Question

if the sum of zeroes of polynomial is -1, where p(x)= (a+1) x square + (2a+3)x + 3a+4, find product of its zeroes

Answer 1

Answer :

The given polynomial is

f (x) = (a + 1)x² + (2a + 3)x + (3a + 4)

If α and β are the zeroes of f (x),

α + β = - (2a + 3)/(a + 1)

⇒ - 1 = - (2a + 3)/(a + 1), given α + β = - 1

⇒ a + 1 = 2a + 3

⇒ 2a - a = 1 - 3

⇒ a = - 2

Now,

αβ = (3a + 4)/(a + 1)

= {3 (- 2) + 4}/(- 2 + 1)

= (- 6 + 4)/(- 1)

= (- 2)/(- 1)

= 2

∴ The product of its zeroes is 2

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Answer 2

Heya !!!


P(X) = (A + 1)X² + ( 2A + 3)X + 3A +4


Here,



A = ( A + 1) , B = ( 2A +3) and C = 3A +4




Sum of zeroes = - B/A



Sum of zeroes = - (2A + 3) / ( A + 1)





-1 = -2A - 3/ A +1



-1( A +1) = -2A -3



-A - 1 = -2A -3



-2A + A = -1 +3




-A = 2


A = -2



And,


Product of zeroes = C/A




Alpha × Beta = 3A +4 / ( A +1)




=> 3 × -2 + 4 / ( -2 + 1)




=> -6 + 4 / -1



=> -2/-1




=> 2


Hence,


Product of zeroes = 2



HOPE IT WILL HELP YOU..... :-)