Question

(3x+6) (x + 1) + 2x = (x+5) (x+4) has
(A) No roots
(C) Real Roots
(B) Imaginary roots
(D) None of these
​

Answer 1

Answer:

(3x+6) (x + 1) + 2x = (x+5) (x+4)

$3 {x}^{2} + 3x + 6x + 6 + 2x = {x}^{2} + 9x + 20$

$3 {x}^{2} + 11x + 6 = {x}^{2} + 9x + 20$

$2 {x}^{2} + 2x - 14= 0 \\ {x}^{2} + x - 7 = 0$

For this quadratic equation

$\sqrt{ {b}^{2} - 4ac} = \sqrt{1 - 4 \times ( - 7)} = \sqrt{29}$

So, the roots are

$x = \frac{ - 1 + \sqrt{29} }{2} \: \: or \: \: \frac{ - 1 - \sqrt{29} }{2}$

The roots are real.