Previous Year Questions

Equation 3:

2x² + 7x + √36 = 0

2x² + 7x + 6 = 0

2x² + 4x + 3x + 6 = 0

2x(x + 2) + 3(x + 2) = 0

(x + 2)(2x + 3) = 0

x = -2, -3/2

Equation 1: ax² + bx + 4 = 0

Equation 2: ax² + 3x + c = 0

Now, Equation 1 + Equation 2 = Equation 3

So, ax² + bx + 4 + ax² + 3x + c = 2x² + 7x + 6

2ax² + (b + 3)x + (4 + c) = 2x² + 7x + 6

Here, 2a = 2 => a = 1

b + 3 = 7 => b = 4

4 + c = 6 => c = 2

Now, Equation 1:

ax² + bx + 4 = 0

x² + 4x + 4 = 0

x² + 2x + 2x + 4 = 0

(x + 2)(x +2) = 0

x = -2, -2

And Equation 2:

x² + 3x + 2 = 0

x² + 2x + x + 2 = 0

(x + 2)(x + 1) = 0

x = -2, -1

a + b + c = 1 + 4 + 2 = 7