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Let , are the roots of the equation a x^2+b x+c=0 where =4 ( >0) . If 3 a=2(c-b) and S= _ r=0 ^ ( ^r ) , then find the value of 3 S .

Correct answer

4

Step-by-step solution

aligned & 3=2 ( c a - b a ) & 3=2 (4 ^2+5 ) 8 ^2+10 -3=0 & 8 ^2+12 -2 -3=0 (2 +3)(4 -1)=0 & = 1 4 =4 =1 & S= 1- = 1 1- 1 4 = 4 3 3 S=4 & aligned

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