Question

if alpha and beta are the roots of the equation(a+1)x2+(2a+3)x + (3a+4)=0. if product of alpha and beta is 2 yhen find sum of alpha and beta

Answer 1

product of quadratic equations is given by c/a
where c is the constant and a is the coefficient of X*2..
a/q
c/a=(3a+4)/(a+1)=2
3a+4=2a+2
a=-2
sum of alpha and beta is given by -b/a
-((2a+3)/(a+1))
put a=-2
answer =-1

Answer 2

Given,

A polynomial p(x) = (a+1)x^2 + (2a+3)x + (3a+4) = 0

Alpha and beta are the roots of p(x).

The product of alpha and beta = 2

To find,

The sum of alpha and beta.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If alpha and beta are the two roots of a quadratic equation p(x) = ax^2 + bx + c, then;

the sum of the roots = (-b)/a

product of the roots = c/a

{Equation-1}

Now, according to the question;

The product of the roots of p(x) = 2

=> Alpha x beta = 2

=> (3a+4)/(a+1) = 2 {according to equation-1}

=> 3a + 4 = 2(a+1) = 2a + 2

=> a = -2

Now, according to equation-1;

The sum of alpha and beta

= -(2a+3)/(a+1)

= -(2×-2 +3)/(-2+1)

= -1

Hence, the sum of alpha and beta is equal to -1.