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Ad libitum [116K]
2 years ago
8

Please help!!! Select the quadratic equation that has no real solution.

Mathematics
1 answer:
Gnom [1K]2 years ago
6 0

Answer:

25x^2-10x+4

Step-by-step explanation:

You can use the quadratic formula to determine if a quadratic equation has real or imaginary solutions. The quadratic formula is: x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. What really matters in this case is the discriminant, which is the stuff under the radical which is: b^2-4ac. This is because the solutions are only imaginary, if the discriminant is negative, because then you would be taking the square root of a negative number. So let's look through each example:

25x^2+20x-4; a=25, b=20, c-4: 20^2-4(25)(-4) = 800. By examining this one example, it's important to note, if you have one negative number as a or c, then it cancels out the negative sign in the -4, and it becomes positive. So let's look at examples where a or c doesn't equal a negative number OR both a and c equal negative, that way they cancel out and over -4ac is still negative.

25x^2-10x+4; a=25, b=-10, c=4. In this case both a and c are positive so -4ac will remain negative. This gives you: (-10)^2-4(25)(4) = 100-400 = -300. So this has a negative discriminant meaning it will have no real solution but rather imaginary solutions

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