Question

Find the condition so that zeros of ax² + bx + c are in the ratio 3:4

Answer 1

$\huge \bold \pink{hello \: mate}$

Let one zero be 3x and the other zero be 4x.

Now, we know that

Sum of the zeroes= -b/a

So ,

3x+4x= -b/a

7x= -b/a

x= -b/7a --------(1)

Also,

Product of the zeroes= c/a

3x×4x= c/a

12x²= c/a

x²=c/12a-------(2)

From (1) and (2),

c/12a= (-b/7a)²

c/12a= b²/49a²

Now, cross multiplying them,

49a²c=12ab²

49ac=12b²

=>49ac-12b² will be the required condition.