Answer:
2 real
Step-by-step explanation:
To answer this question, we need to know whether the discriminant is positive, negative, or zero. The discriminant is the part of the quadratic equation that is under the square root.
Quadratic Equation: -b±√(b²-4ac)/(2)
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b²-4ac is the discriminant
The equation is already in Standard Form, so now we need to find the a, b, and c values.
- Standard Form: [tex]0 = ax^{2} +bx+c[/tex]
- [tex]x^{2} -7x+3 = 0[/tex]
- A = 1 (since an imaginary 1 is in front of the variable)
- B = -7
- C = 3
Now we substitute these numbers into the discriminant ( b²-4ac ):
- (-7)²-4(1)(3)
- -7²= 49
- 4(1)(3) = 12
- So, we have 49-12 = 37
- This is a positive result! (37)
A positive discriminant = two real solutions
A discriminant of zero = one real solution
A negative discriminant = zero real solutions (it would equal nonreal complex solutions instead)
I hope this helps!
