Question

For what value of k, will the equation 2x2 – 2(1 +2k )x + (3 + 2k) = 0 have real but distinct roots ? when will the roots be equal?​

Answer 1

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: