SOLUTION: When using the quadratic formula to solve a quadratic equation
ax(squared)+bx+c=0, the discriminant is b squared-4ac. This discriminant can be positive, zero, or negative.
Please
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Question 85503This question is from textbook College Algebra 4th/e
: When using the quadratic formula to solve a quadratic equation
ax(squared)+bx+c=0, the discriminant is b squared-4ac. This discriminant can be positive, zero, or negative.
Please explain what the value of the discriminant means to the graph of y=ax squared bx+c.Choose the values of a,b and c to create a discriminant and graph the corresponding equation.
I do greatly appreciate your website and assistance.
This question is from textbook College Algebra 4th/e
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If the discriminant is greater than zero, then you will have a positive square root. This means you will have 2 roots that are real numbers.
Ex: x^2+5x+6 if you put this into the quadratic equation you get
This further shows that the roots are real numbers of x=-2 and x=-3
2 real roots
If the discriminant is equal to zero, then you will have only 1 root with multiplicity of 2.
Ex: x^2+4x+4 place into quadratic formula
1 real root with multiplicity of 2
If you have a negative discriminant, then no real roots will result since it's not possible to take the square root of a negative number and get a real result.
Ex: x^2+x+3 if placed into the quadratic formula
No real roots, only complex roots
So a you will have a graph that doesn't cross the x-axis but will have complex roots
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