Question

if the roots of the equation 12x^2-mx+b=0 are in the ratio 2:3 then find m

Answer 1

↑ Here is your answer ↓
_____________________________________________________________
_____________________________________________________________

$12x^2-mx+b=0$

The zeroes are '2a' and '3a'

We know that sum of roots = -b/a

$2a + 3a = m/12$

$5a = m/12$

$60a = m$

$a = m/60$

$a^2 = m^2/3600$

Now,

Product of roots = c/a

$2a * 3a = b/12$

$6a^2 = b/12$

$72a^2 = b$

$a^2 = b/72$

Now equate a²

$b/72 = m^2/3600$

$3600b = 72m^2$

$m^2 = 3600b/72$

$m^2 = 50b$

$m = \sqrt{50b}$

____________________________________________________________________________________________________________________________

Glad to help you.
@EmadAhamed