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<u>Question:</u>
Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0
<u>Answer:</u>
The number of real solutions for the equation is zero
<u>Solution:</u>
For a Quadratic Equation of form : ---- eqn 1
The solution is
Now , the given Quadratic Equation is ---- eqn 2
On comparing Equation (1) and Equation(2), we get
a = 1 , b = 5 and c = 7
In ,
is called the discriminant of the quadratic equation
Its value determines the nature of roots
Now, here are the rules with discriminants:
1) D > 0; there are 2 real solutions in the equation
2) D = 0; there is 1 real solution in the equation
3) D < 0; there are no real solutions in the equation
Now let solve for given equation
Since -3 is less than 0, this means that there are 0 real solutions in this equation.