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
![b to the power of 2 end exponent minus 4 a c equals open parentheses negative 8 close parentheses to the power of 2 end exponent minus 4 blank cross times blank 4 blank cross times blank 2](data:image/png;base64,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)
= 64 - 32
= 32 > 0
The discriminant is greater than zero, so it has two real solutions.
We know the qadratic formula x = [-b±√(b2-4ac)]/2a