## anonymous 3 years ago How would you describe the roots of a quadratic equation?

1. anonymous

Like: $\frac{ -3\pm \sqrt{17} }{ 4 }$

2. mathmate

Graphically, they (real zeroes) cross the x-axis. If the zeroes are complex, they do not touch the x-axis.. Numerically, the roots, x1 and x2, have the property that f(x1)=0 and f(x2)=0, where f(x)=0 is the quadratic equation.

3. anonymous

|dw:1358090824515:dw|

4. anonymous

|dw:1358090914575:dw|

5. anonymous

the roots describe the values of x for which the required quadratic function's value is zero.

6. hba

Actually we use the discriminant to determine, $\huge\ D=b^2-4ac$

7. anonymous

@hba Thats what i got as the discriminant

8. hba

$b^2-4ac>0,two \ real \ solutions$$b^2-4ac=perfect \ squar e ,Two \ real \ rational \ solutions$

9. hba

If, $b^2-4ac= no \ perfect \ sq uare,Two \ real \ irrational \ solutions$

10. hba

$b^2-4ac=0,One \ real \ solution$

11. hba

$b^2-4ac<0,No \ real \ but \ two \ imaginary \ solutions$

12. anonymous

Thanks! @hba

13. hba

You are welcome :)