The following quadratic equations have two real solutions:
-x² = 4 - 5x ⇒ B
2x² - 8x = 24 ⇒ C
5x² - 10x + 3 = 0 ⇒ D
Step-by-step explanation:
The quadratic equation ax² + bx + c = 0 has real solutions if:
To solve the problem put the quadratic equation in the form ax² + bx + c = 0, then find the values of a, b and c and substitute them in the rule b² - 4ac, if the answer is positive or zero then the quadratic has a real solution if the answer is negative then the quadratic has no real solutions
A.
∵ 9x² - 12x + 4 = 0
∴ a = 9, b = -12, c = 4
- Substitute them in b² - 4ac
∵ (-12)² - 4(9)(4) = 144 - 144 = 0
∴ b² - 4ac = 0
∴ The equation 9x² - 12x + 4 = 0 has one real solutions
B.
∵ -x² = 4 - 5x
- Add 5x to both sides
∴ -x² + 5x = 4
- Subtract 4 from both sides
∴ -x² + 5x - 4 = 0
∴ a = -1, b = 5, c = -4
- Substitute them in b² - 4ac
∵ (5)² - 4(-1)(-4) = 25 - 16 = 9
∴ b² - 4ac > 0
∴ The equation -x² = 4 - 5x has two real solutions
C.
∵ 2x² - 8x = 24
- Subtract 24 from both sides
∴ 2x² - 8x - 24 = 0
∴ a = 2, b = -8, c = -24
- Substitute them in b² - 4ac
∵ (-8)² - 4(2)(-24) = 64 - (-192) = 64 + 192 = 256
∴ b² - 4ac > 0
∴ The equation 2x² - 8x = 24 has two real solutions
D.
∵ 5x² - 10x + 3 = 0
∴ a = 5, b = -10, c = 3
- Substitute them in b² - 4ac
∵ (-10)² - 4(5)(3) = 100 - 60 = 40
∴ b² - 4ac > 0
∴ The equation 5x² - 10x + 3 = 0 has two real solutions
E.
∵ x² - 2x = -5
- Add 5 to both sides
∴ x² - 2x + 5 = 0
∴ a = 1, b = -2, c = 5
- Substitute them in b² - 4ac
∵ (-2)² - 4(1)(5) = 4 - 20 = -16
∴ b² - 4ac < 0
∴ The equation x² - 2x = -5 has no real solution
The following quadratic equations have two real solutions:
-x² = 4 - 5x
2x² - 8x = 24
5x² - 10x + 3 = 0
Learn more:
You can learn more about the quadratic equations in brainly.com/question/8196933
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