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Question

Determine $$P$$, so that the following equation has coincident roots: $$t^{2}+p^{2}=2(p+1)t$$.


Solution

Given,

$$t^2+p^2=2(p+1)t$$

$$\Rightarrow t^2-2(p+1)t+p^2=0$$

condition for roots to be coincident is,

$$b^2-4ac=0$$

$$[-2(p+1)]^2=4(1)(p^2)$$

$$4(p+1)^2=4p^2$$

$$p^2+1+2p=p^2$$

$$\Rightarrow p=-\dfrac{1}{2}$$

Mathematics

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