Question

Under what condition both the roots of the equation ax^2+bx+c=0 are zero?​

Answer 1

Step-by-step explanation:

Given :-

ax²+bx+c = 0

To find :-

The condition for both roots of the equation are zero.

Solution :-

Given quadratic equation is ax²+bx+c = 0

By quadratic formula ,

The roots are x = [-b±√(b²-4ac)]/2a

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

Case-1:-

If b = 0 then

=> 0²-4ac = 0

=> 0-4ac = 0

=> -4ac = 0

=> ac = 0/-4

=> ac = 0

=> a = 0 or c = 0

Case-2:-

If a = 0 then the quadratic equation can't be exist .

So, the required condition is b = 0 and c = 0

Check :-

If b = c = 0 then ax²+bx+c = 0 becomes

=> ax²+0(x)+0 = 0

=> ax²+0+0 = 0

=> ax² = 0

=> x² = 0/a

=> x² = 0

=> x = 0

The roots are 0 and 0

Answer :-

The condition for both roots are zero of the equation ax²+bx+c = 0 is b = 0 and c = 0