Rookies turn to math problems Why does equation 2 (a + 1) x ^ 2 + 4ax + 2a-1 = 0 have only one real root?

Rookies turn to math problems Why does equation 2 (a + 1) x ^ 2 + 4ax + 2a-1 = 0 have only one real root?

Let B ^ 2-4ac = 0, that is: (4a) ^ 2-4 * 2 (a + 1) * (2a-1) = 0, then a = 1
When it is a one variable linear equation, use the verification method: 2 (a + 1) = 0, a = - 1, then, 4ax + 2a-1 = 0, x = - 3 / 4 also has only one real root. So when it is a one variable quadratic equation, a = 1, when it is a one variable linear equation, a = - 1

Take out 200 yuan to buy pens and notebooks, 3 yuan for each pen and 5 yuan for each notebook. You need to buy 48 pens and notebooks in total. The number of notebooks should not be less than the number of pens. How many plans do you have? Please list them one by one?
You big brother and big sister, help little brother this math rookie!

Have you learned equation? This kind of problem is usually solved by equation. Suppose you buy x pens and Y notebooks. According to the meaning of 3x + 5Y ≤ 200y ≥ XX + y = 48, buy 24 notebooks, 24 pens 192 yuan buy 25 notebooks, 23 pens 194 yuan buy 26 notebooks, 22 pens 196 yuan buy 27 notebooks, 21 pens 198 yuan

That math master, help me this math rookie
Xiaojie's mother paid 69 yuan less than the original price when she bought something with 70% discount. What was the original price of the thing?

Let X be the original price
Then (100-70)% x = 69
x=230