All Plus Signs

Algebra Level 2

x 2 + x − 123456789 = 0 \large x^2 + x - 123456789 = 0

The equation above has __________ \text{\_\_\_\_\_\_\_\_\_\_} .

Two non-real roots One real root only Two distinct real roots

Chung Kevin by Chung Kevin , 45, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Clearly, the equation above has a discriminant b 2 − 4 a c = 1 + 4 ⋅ 123456789 > 0 ⇒ b^2 - 4ac = 1 + 4\cdot 123456789 > 0 \Rightarrow the equation above has two distinct real solutions (roots).

4 Helpful 0 Interesting 0 Brilliant 0 Confused

For the quadratic equation A x 2 + B x + C = 0 Ax^2 + Bx + C = 0 ,

if B 2 = 4 A C B^2 = 4AC , the roots are equal

if B 2 > 4 A C B^2 > 4AC , the roots are real and distinct

if B 2 < 4 A C B^2 < 4AC , the roots are imaginary or non-real.

x 2 + x − 123456789 = 0 x ^2 + x - 123456789 = 0 ⟹ \implies B 2 > 4 A C B^2 > 4AC ∴ \therefore The roots are real and distinct.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...