Mathematics
Grade10
Easy
Question
How many solutions are there for the equation
using the discriminant?
- 0
- 1
- 2
- Either 1 or 2.
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 4 x plus 3 equals 0](data:image/png;base64,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)
Now,
![b to the power of 2 end exponent minus 4 a c equals 4 to the power of 2 end exponent minus 4 blank cross times blank 1 blank cross times blank 3](data:image/png;base64,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)
![equals 4 greater than 0](data:image/png;base64,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)
The discriminant value is greater than zero, so it has two real solution.
The discriminant is the part of the quadratic formula found within the square root.