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SSSSS [86.1K]
3 years ago
12

9/20

Mathematics
1 answer:
Stella [2.4K]3 years ago
4 0

<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 x^{2}+5 x+7=0 is zero

<u>Solution:</u>

For a Quadratic Equation of form : a x^{2}+b x+c=0  ---- eqn 1

The solution is x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}  

Now , the given Quadratic Equation is x^{2}+5 x+7=0  ---- eqn 2

On comparing Equation (1) and Equation(2), we get

a = 1 , b = 5 and c = 7

In x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} , b^2 - 4ac 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

D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

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