y = 12x2 - 9x + 4 how many real solution 10x + y = -x2 + 2 how many real solution(s) 4y - 7 = 5x2 - x + 2 + 3y how many real sol
ution(s) y = (-x + 4)2 how many real solution(s)
1 answer:
Answer:
(a) 0
(b) 2
(c) 0
(d) 1
Step-by-step explanation:
All of these can be solved easily by a graphing calculator. The attached graphs show the real solutions of those equations that have them. Here, you can also answer the question from the sign of the discriminant.
For y = ax² +bx +c
the value of the discriminant is
... b² -4ac
When the discriminant is negative, both solutions are complex. When 0, there is one solution. When positive, there are two real solutions.
(a) The discriminant is ...
... (-9)² -4(12)(4), a negative number. There are no real solutions.
(b) This needs to be rearranged to ...
... y = -x² -10x +2
Then the discriminant is ...
... (-10)² -4(-1)(2), a positive number. There are 2 real solutions.
(c) This needs to be rearranged to ...
... y = 5x² -x +9 . . . . add 7-3y
Then the discriminant is ...
... (-1)² -4(5)(9), a negative number. There are no real solutions.
(d) This equation is in vertex form, and the vertex is (4, 0). Since the vertex is the only x-intercept, there is one real solution.
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