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

Question

If the sum of the roots of the equation (a+1)x2+(2a+3)x+(3a+4)=0, where a ≠ -1 , is -1, then the product of the roots is (A) 4 (B) 2 (C) 1 (D) -2

Tardigrade Admin · Accepted Answer

Given equation is, (a+1) x2+(2 a+3) x+(3 a+4)=0 ; a ≠-1 and sum of the roots =-1 ⇒ -((2 a+3)/(a+1))=-1 ⇒ 2 a+3=a+1 ⇒ a=-2 ∴ Product of the roots =(3 a+4/a+1)=(3(-2)+4/-2+1) (∵ a=-2) = (-6+4/-1)=2

Q. If the sum of the roots of the equation $(a + 1) x^{2} + (2 a + 3) x + (3 a + 4) = 0,$ where a $\neq =$ $- 1$ , is $- 1$ , then the product of the roots is

4

2

1

-2

-4

Q. If the sum of the roots of the equation (a+1)x2+(2a+3)x+(3a+4)=0, where a = −1 , is −1, then the product of the roots is

4

2

1

-2

-4

Given equation is, (a+1)x2+(2a+3)x+(3a+4)=0 ; a=−1 and sum of the roots =−1 ⇒−(a+1)(2a+3)​=−1 ⇒2a+3=a+1 ⇒a=−2 ∴ Product of the roots =a+13a+4​=−2+13(−2)+4​ (∵a=−2) =−1−6+4​=2

Q. If the sum of the roots of the equation $(a + 1) x^{2} + (2 a + 3) x + (3 a + 4) = 0,$ where a $\neq =$ $- 1$ , is $- 1$ , then the product of the roots is