Question

If the sum of the roots of the equation ( a+ 1 ) x² +( 2a + 3 )x + (3a + 4) = 0 , then find the product of the roots

Answer 1

Heya user,

Considering α & β as roots and -->
---> α + β = -1
By Viete's relation or by Roots-Coefficient relation,
----> α + β = -[ 2a + 3 ] / [ a + 1 ]
===> -1 = -[ 2a + 3 ] / [ a + 1 ]
===> a + 1 = 2a + 3;
===> a = -2;

Now, αβ = [ 3a + 4 ] / [ a + 1 ] = [ 3*-2 + 4 ] / [ -2 + 1 ] = -2 / -1 = 2

Hence, product of roots is 10/3 = 1.3333....

Answer 2

★ QUADRATIC RESOLUTION ★

Given function :

( a + 1 ) x² +( 2a + 3 )x + 3a + 4 = 0

Sum of the roots = -1

- [( 2a + 3 ) / a + 1 ]

HENCE , a = -2

Therefore , product of roots -

-6 + 4 / -2 + 1

2

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