At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
System of equations y = x² + 7x + 4 has one real root with the line y = x -5.
What is the discriminant in the quadratic equation?
A quadratic equation is the polynomial equation of two degrees in one variable. The general form of a quadratic equation is ax² + bx + c = 0.
The quadratic equation formula for the solution of roots.
[tex]\rm (\alpha ,\beta ) = [ -b[/tex]±[tex]\rm \sqrt{b^{2} - 4ac} /2ac[/tex]]
The discriminant is the [tex]\rm \sqrt{b^{2} - 4ac}[/tex] part of the quadratic equation
If D is greater than zero then the roots are real and distinct.
If D is equal to zero then the roots are real and equal.
If D is less than zero then the roots are imaginary and unequal.
y = x² + 7x + 4
From First option, System of equations
y = x² + x – 4
y = x – 5
So, x - 5 = x² + x – 4
x² + x – 4 - x + 5 = 0
x² + 1 = 0
discriminant = b²- 4×a×c
= 0²- 4×1×1
-4 < 0, therefore the equation has no real roots.
From Second option, System of equations
y = x² + 2x – 1
y = x – 5
So, x - 5 = x² + 2x – 1
x² + 2x - 1 - x + 5 = 0
x² + x + 4 = 0
discriminant = b²- 4×a×c
= 1²-4×1×4
-15 < 0 therefore, the equation has no real roots.
From Third option, System of equations
y = x² + 6x + 9
y = x – 5
So, x - 5 = x² + 6x + 9
x² + 6x + 9 - x + 5 = 0
x² + 5x + 4 = 0
discriminant = b²- 4×a×c
= 5²-4×1×4
9 > 0 therefore, the equation has two different real roots.
From Fourth option, System of equations
y = x² + 7x + 4
y = x – 5
So. x - 5 = x² + 7x + 4
x² + 7x + 4 - x + 5 = 0
x² + 6x + 9 = 0
discriminant = b²- 4×a×c
= 6²-4×1×9 = 0
0 therefore, the equation has one real root.
Since, System of equations y = x² + 7x + 4 has one real root with the line y = x -5.
Learn more about quadratic equations;
https://brainly.com/question/2263981
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
