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The-roots-of-x-2-a-1-x-b-2-0-are-equal-Then-which-of-the-following-can-be-the-values-of-a-and-b-




Question Number 27397 by julli deswal last updated on 06/Jan/18
The roots of x^2 −(a+1)x+b^2 =0 are  equal. Then which of the following  can be the values of  a  and  b  .
$$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:{x}^{\mathrm{2}} −\left({a}+\mathrm{1}\right){x}+{b}^{\mathrm{2}} =\mathrm{0}\:\mathrm{are} \\ $$$$\mathrm{equal}.\:\mathrm{Then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\:{a}\:\:\mathrm{and}\:\:{b}\:\:. \\ $$
Answered by jota@ last updated on 06/Jan/18
a=1  and b=1
$${a}=\mathrm{1}\:\:{and}\:{b}=\mathrm{1} \\ $$
Answered by mrW1 last updated on 06/Jan/18
Δ=(a+1)^2 −4b^2 =0  ⇒a+1=±2b  ⇒a=±2b−1
$$\Delta=\left({a}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{4}{b}^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow{a}+\mathrm{1}=\pm\mathrm{2}{b} \\ $$$$\Rightarrow{a}=\pm\mathrm{2}{b}−\mathrm{1} \\ $$

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