For what value of k, will the equation 2×2 – 2(1 +2k )x + (3 + 2k) = 0 have real but distinct roots ? when will the roots be equal?​

Question

For what value of k, will the equation 2×2 – 2(1 +2k )x + (3 + 2k) = 0 have real but distinct roots ? when will the roots be equal?​

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Rose 1 month 2021-08-13T13:44:28+00:00 1 Answer 0 views 0

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    2021-08-13T13:46:26+00:00

    Answer:

    Start by computing its discriminant[1] (in reduced form since you have a first order term  2k ) Δ′ .

    Δ′=k2−3(k−1)  

    To prove that the equation has two distinct real roots, you only need to show that:  ∀k∈R,Δ′>0  

    This is easily done by noticing that:  k2−3(k−1)=(k−32)2+54  which is always  >0 .

    I hope this helps!

    Step-by-step explanation:

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