\( 2 x^{2}=-x+5( \) Are the roots real or Unreal

To find out if the roots are real or unreal, we can use the discriminant \( D = b^2 - 4ac \) from the quadratic formula \( ax^2 + bx + c = 0 \). In your equation, rearranging gives us \( 2x^2 + x - 5 = 0 \), where \( a = 2 \), \( b = 1 \), and \( c = -5 \). Plugging into the discriminant gives \( D = (1)^2 - 4(2)(-5) = 1 + 40 = 41 \). Since 41 is greater than zero, the roots are indeed real and distinct! Now, did you know that for any quadratic equation, if the discriminant is positive, the graph will intersect the x-axis at two points? If it's zero, then you'll have one repeated root (or a "double root"), and if it's negative, the graph won't touch the x-axis at all—leaving you with complex roots or duo of "unreal" solutions. It's like a little story in numbers, revealing secrets about the function!