Answer:
Put the equation in standard form by bringing the 4x + 1 to the left side.
7x2 - 4x - 1 = 0
We use the discriminant to determine the nature of the roots of a quadratic equation. The discriminant is the expression underneath the radical in the quadratic formula: b2 - 4ac.
b2 - 4ac In this case, a = 7, b = -4, and c = -1
(-4)2 - 4(7)(-1)
16 + 28 = 44
Now here are the rules for determining the nature of the roots:
(1) If the discriminant = 0, then there is one real root (this omits the ± from the quadratic formula, leaving only one possible solution)
(2) If the discriminant > 0, then there are two real roots (this keeps the ±, giving you two solutions)
(3) If the discriminant < 0, then there are two imaginary roots (this means there is a negative under the radical, making the solutions imaginary)
44 > 0, so there are two real roots
Step-by-step explanation:
Let's rewrite the given equation such that only y is on the left side and everything else on the right side:
Simplifying this by dividing by 6, we get
This line has a slope of -1/2, which means that a line perpendicular to this has a slope of 2 (i.e., negative reciprocal). So we can write its equation as
This is the slope-intercept form of the equation of the line perpendicular to our given line. To complete this form, we need to find the value of b. Since this line passes through (1, -7), put these numbers into our equation to get
Therefore, the slope-intercept form of the equation can be written as
7
When you do 27 times x squared times z all over -3, then times that by x squared times z to the sixth power, you get -9x^4z^7
