I am having trouble with these. I don't even know where to start:
Find the exact solutions to 6x^2+x+4=0 By using the Quadratic Formula.
Find the value of the discriminant for 9x^2+1=6x. Then describe the number and type of roots for the equation.
Thanks =)
Start the first by using the quadratic formula.
http://www.purplemath.com/modules/quadform.htm
In the second, put the quadratic in standard form (ax^2 +bx +c), and compute the descriminant.
http://www.mathnstuff.com/math/spoken/here/2class/320/quadequ.htm
No problem! I can help you with both of these problems.
Problem 1: Find the exact solutions to 6x^2+x+4=0 by using the Quadratic Formula.
Step 1: Identify the coefficients of the quadratic equation. In this case, we have a = 6, b = 1, and c = 4.
Step 2: Write down the Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / (2a)
Step 3: Substitute the values of a, b, and c into the Quadratic Formula:
x = (-(1) ± √((1)^2 - 4(6)(4))) / (2(6))
Step 4: Simplify the expression inside the square root:
x = (-1 ± √(1 - 96)) / 12
x = (-1 ± √(-95)) / 12
Step 5: Since we have a square root of a negative number, we know that the equation does not have real solutions, but has complex solutions.
Therefore, the exact solutions to the equation 6x^2+x+4=0 are:
x = (-1 + √(-95)i) / 12
x = (-1 - √(-95)i) / 12
Problem 2: Find the value of the discriminant for 9x^2+1=6x. Then describe the number and type of roots for the equation.
Step 1: Write the equation in standard quadratic form: 9x^2 - 6x + 1 = 0
Step 2: Identify the coefficients of the quadratic equation. In this case, we have a = 9, b = -6, and c = 1.
Step 3: Calculate the discriminant, which is given by the formula: Δ = b^2 - 4ac.
Substitute the values of a, b, and c into the formula:
Δ = (-6)^2 - 4(9)(1)
Δ = 36 - 36
Δ = 0
Step 4: Analyze the value of the discriminant:
If the discriminant (Δ) is equal to 0, then the quadratic equation has exactly one real root.
If the discriminant (Δ) is positive, then the quadratic equation has two distinct real roots.
If the discriminant (Δ) is negative, then the quadratic equation has two complex roots.
In this case, since the discriminant is Δ = 0, we know that the equation 9x^2+1=6x has exactly one real root.
I hope this explanation helps! Let me know if you have any further questions or need additional assistance.