Mathematics
Grade10
Easy
Question
How many solutions are there for the equation
using the discriminant?
- 0
- 1
- 2
- 3
Hint:
Any equation of the form p (x) = 0, where p (x) is a polynomial of degree 2, is a quadratic equation
The correct answer is: 2
Step 1 of 1:
We have given a quadratic equation ![x to the power of 2 end exponent plus 5 x plus 2 equals 0](data:image/png;base64,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)
![b to the power of 2 end exponent minus 4 a c equals open parentheses 5 close parentheses to the power of 2 end exponent minus 4 cross times 1 cross times 2](data:image/png;base64,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)
![equals 25 minus 8](data:image/png;base64,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)
![equals 17 greater than 0](data:image/png;base64,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)
The discriminant is greater than zero, so it has two real solutions.
The discriminant is the part of the quadratic formula found within the square root.