The equation 3 x 2 + x + 5 = x - 3 , where x ⁡ is real, has

Step-by-step solution

3 x 2 + x + 5 = x - 3           . . . 1 We know that for a quadratic expression a x 2 + b x + c ,   a > 0 , if discriminant i.e. D = b 2 - 4 a c < 0 , then the quadratic is always positive for all real values of the variable. Now, consider 3 x 2 + x + 5 We have, discriminant = b 2 - 4 a c = 1 - 4 × 3 × 5 < 0 ∴   3 x 2 + x + 5 > 0 ,   ∀   x ∈ R Squaring 1 , we get, 3 x 2 + x + 5 = x - 3 2 ⇒ 3 x 2 + x + 5 = x 2 - 6 x + 9 &#