Question

Does the parabola with equation x2– x + 6 = 0 have real or imaginary roots?

Answer 1

imaginary roots

to check the nature of the roots of a parabola in standard form :

ax² + bx + c = 0 : ( a ≠ 0 ) use the discriminant b² - 4ac

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are not real

for x² - x + 6 = 0 with a = 1, b = - 1, c = 6

b² - 4ac = ( -1)² - (4 × 1 × 6 ) = 1 - ( 24 ) = 1 - 24 = - 23

since b² - 4ac < 0 then roots are not real ( imaginary )