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Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let a, b be the roots of the quadratic equation x^2-(k-2) c x-(k-1) d=0 and c, d be the roots of the quadratic equation x^2-(k-2) a x-(k-1) b=0 . If a, b, c and d are distinct, non-zero real numbers such that a+b+c+d=100 , then find the integral value of k .

Correct answer

6

Step-by-step solution

a+b=(k-2) c ...(1) a b=-(k-1) d ...(2) c+d=(k-2) a ...(3) c d=-(k-1) b ...(4) Substitute Eqn. (1), (3) to (2) aligned a((k-2) c-a) & =-(k-1)((k-2) a-c) (k-2) a c-a^2 & =-(k-1)(k-2) a+(k-1) c ...(5) aligned Substitute Eqn. (1), (3) to (4) c((k-2) a-c)=-(k-1)((k-2) c-a) (k-2) a c-c^2=-(k-1)(k-2) c+(k-1) a ...(6) Eqn. (6) - Eqn. (5) aligned a^2-c^2 & =(k-1)(k-2)(a-c)+(k-1)(a-c) a+c & =(k-1)^2 (k-2)(k-1)^2 & =100 k^3-4 k^2+5 k-102 & =0 (k-6) (k^2+2 k+17 ) & =0 k & =6 aligned

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