Question

Find sum of zeros of polynomial ax2+2x+3a if sum of zero is equal to their product

Answer 1

hello users .......

we have given that:-

for a quadratic equation :: ax² + 2x + 3a = 0 

the sum  and the product of roots are equal ;

solution:-
here;
we know that : 
For a quadratic equation : ax² + bx + c = 0

sum of roots = - b / a ;
and
product of roots = c / a 

here,
sum of roots = - b / a =  - 2 / a 
and 
product of roots = c / a =  3a / a = 3

According to question ;
sum of roots = product of roots 

=> -2 / a = 3

=> a = -2 / 3 


now; put the value of a in the givn equation .
we get ,
(-2 / 3) x² + 2x + ( -2 / 3) = 0 

=>- 1/3  (2 x² - 6x +2 ) = 0 ...taking (-1/3) common ;

hence;
the required quadratic equation is : 2x² - 6x + 2 = 0 answer 

✰✰ hope it helps ✰✰

Answer 2

Answer:

Step-by-step explanation:

From the equation we get,

a=a, b=2, c=3a

Let Roots of the equation be m and n.

so, m+n =-b/a. mn =c/a,

-2/a ÷3a/a

-2/3a

a=-2/3