Mathematics
Grade10
Easy
Question
Find the number of solutions obtained to the quadratic equation using the discriminant.
- 0
- 1
- 2
- Either 0 or 1
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 an equation
![negative 4 x to the power of 2 end exponent plus 16 x minus 12 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 negative 16 close parentheses to the power of 2 end exponent minus 4 blank cross times blank minus 4 blank cross times blank minus 12](data:image/png;base64,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)
![equals 256 minus 192](data:image/png;base64,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)
![equals 64 greater than 0](data:image/png;base64,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)
The discriminant is the part of the quadratic formula found within the square root.