Let ^2 and ^2 are roots of the quadratic equation a x^2+b x+c=0 and b^2-c^2 a c = . If solution set of the inequality _ (8 x)

Question

Let ^2 and ^2 are roots of the quadratic equation a x^2+b x+c=0 and b^2-c^2 a c = . If solution set of the inequality _ (8 x) < 1 in (0,2 ) is ( , ) ( , ) , then find the value of ( + ) .

Quantrex Academy · Accepted Answer

Correct answer: 5

^2 + ^2 =-b / a ...(1) ^2 ^2 =c / a ...(2) aligned & Now, Eqn. (1) ^2 Eqn. (2) & b^2-c^2 a^2 = ( ^2 + ^2 )^2- ( ^2 ^2 )^2 & b^2-c^2 a^2 = ( ^2 + ^2 + ^2 ^2 ) ( ^2 + ^2 - ^2 ^2 ) & b^2-c^2 a^2 = (2 ^2 ) (2 ^2 )= 4 c a & b^2-c^2 a c =4 =4 aligned Now, ₄(8 x) < 1 aligned & 0 < x < 1 / 2 & x (0, / 6) (5 / 6, ) ( , ) ( , ) & + aligned + =5+0=5

Let ^2 and ^2 are roots of the quadratic equation a x^2+b x+c=0 and b^2-c^2 a c = . If solution set of the inequality _ (8 x) < 1 in (0,2 ) is ( , ) ( , ) , then find the value of ( + ) .

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