Question

Solve the equation using the quadratic formula.

10x²-x+9=0
3
2
B) x = ±3
A) X=
c) No Solution
D x=9

Answer 1

Answer: C) No solution

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Step-by-step explanation:

Compare the given equation to the format of:
`a\text{x}^2+b\text{x}+c`

We have,

• a = 10
• b = -1
• c = 9

Plug those values into the quadratic formula below.

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(-1)\pm√((-1)^2-4(10)(9)))/(2(10))\\\\x = (1\pm√(-359))/(20)\\\\`

The discriminant
`d = b^2 - 4ac = (-1)^2-4(10)(9) = -359` is negative, so there are no real numbered solutions. The two solutions are complex numbers in the form a+bi where
`i = √(-1)`.

If your teacher has not covered imaginary numbers or complex numbers yet, then the final answer would be "No solution"

Visually, you could use a graphing calculator (or something like Desmos) to plot out the parabola. The parabola
`10\text{x}^2-\text{x}+9` never crosses the x axis. This fact visually indicates there are no real solutions.