Question

if the sum of the roots of the equation ax^+4x+c=0 is half of their difference,then the value of ac is...

Answer 1

Quadratic formula

x=(1/2a)(-4+/-sqrt(16-4ac)

Add the roots

(1/2a))[-4+sqrt(16-4ac)-4-sqrt(16-4ac)]=(1/2a)(-8)=-4/a

Subtract the roots

(1/2a)[-2sqrt(16-4ac)]=-sqrt(16-4ac)/a

Half the difference is -sqrt(16-4ac)/2a

That equals the sum, -4/a or -8/2a

They equal each other

-8=-sqrt(16-4ac)

multiply by -1 and square both sides

 

64=16-4ac

48=-4ac

ac=-12

If a is 1, then c is -12

The equation is x^2+4x-12=0

that factors into (x+6) and (x-2)

roots -6 and 2 sum to -4.

The difference is -8, so the sum is half the difference.  

Hope helps.......

Answer 2

Step-by-step explanation:

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