If the functions f(x)=(k2−3k+2)x2+(k2−1) ∀x∈R and g(x)=(k2−6k+5)x3+(k2−2k+1)x+(k2−k) ∀x∈R have the same graph, then the number of real values of k, is:

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If the functions $f (x) = (k^{2} - 3 k + 2) x^{2} + (k^{2} - 1) \forall x \in R$ and $g (x) = (k^{2} - 6 k + 5) x^{3} + (k^{2} - 2 k + 1) x + (k^{2} - k) \forall x \in R$ have the same graph, then the number of real values of k, is:

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answer is 1.

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$k^{2} - 3 k + 2 = 0, k^{2} - 1 = 0, k^{2} - 6 k + 5 = 0, k^{2} - 2 k + 1 = 0$

and $k^{2} - k = 0$ must be satisfied simultaneously.
So, $k = 1$
Hence, number of real values of k is one (i.e., k=1)

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