Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To determine the number of real number solutions for the quadratic equation [tex]\(-4j^2 + 3j - 28 = 0\)[/tex], we can use the discriminant of the quadratic formula.
The standard form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex]. Here, the coefficients are:
- [tex]\(a = -4\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -28\)[/tex]
The discriminant ([tex]\(\Delta\)[/tex]) is given by the formula:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the formula:
[tex]\[ \Delta = (3)^2 - 4(-4)(-28) \][/tex]
[tex]\[ \Delta = 9 - 4 \cdot (-4) \cdot (-28) \][/tex]
[tex]\[ \Delta = 9 - 4 \cdot 4 \cdot 28 \][/tex]
[tex]\[ \Delta = 9 - 449 \][/tex]
[tex]\[ \Delta = -439 \][/tex]
Now, we examine the value of the discriminant:
- If [tex]\(\Delta > 0\)[/tex], there are 2 real solutions.
- If [tex]\(\Delta = 0\)[/tex], there is 1 real solution.
- If [tex]\(\Delta < 0\)[/tex], there are no real solutions.
Since [tex]\(\Delta = -439\)[/tex], which is less than 0, there are no real number solutions.
The best answer for the question is:
A. 0
The standard form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex]. Here, the coefficients are:
- [tex]\(a = -4\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -28\)[/tex]
The discriminant ([tex]\(\Delta\)[/tex]) is given by the formula:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the formula:
[tex]\[ \Delta = (3)^2 - 4(-4)(-28) \][/tex]
[tex]\[ \Delta = 9 - 4 \cdot (-4) \cdot (-28) \][/tex]
[tex]\[ \Delta = 9 - 4 \cdot 4 \cdot 28 \][/tex]
[tex]\[ \Delta = 9 - 449 \][/tex]
[tex]\[ \Delta = -439 \][/tex]
Now, we examine the value of the discriminant:
- If [tex]\(\Delta > 0\)[/tex], there are 2 real solutions.
- If [tex]\(\Delta = 0\)[/tex], there is 1 real solution.
- If [tex]\(\Delta < 0\)[/tex], there are no real solutions.
Since [tex]\(\Delta = -439\)[/tex], which is less than 0, there are no real number solutions.
The best answer for the question is:
A. 0
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.