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Prove that for all positive k < 1, the equation (x + a) (x + b) = k (x + c)² has two real roots, for any real a, b, c. |
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Answer» The quadratic will have real root only when its DISCRIMINANT will be greater than or EQUAL to 0Discriminant of GIVEN equation =b 2 −4ac =(−8) 2 −4×1×k>0⇒64−4k>0⇒4k<64⇒k<16So, the value of k should be less than 16. |
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