Answer:
√(p²-4q)
Step-by-step explanation:
Using the Quadratic Formula, we can say that
x = ( -p ± √(p²-4(1)(q))) / 2(1) with the 1 representing the coefficient of x². Simplifying, we get
x = ( -p ± √(p²-4q)) / 2
The roots of the function are therefore at
x = ( -p + √(p²-4q)) / 2 and x = ( -p - √(p²-4q)) / 2. The difference of the roots is thus
( -p + √(p²-4q)) / 2 - ( ( -p - √(p²-4q)) / 2)
= 0 + 2 √(p²-4q)/2
= √(p²-4q)
Answer:
x = 21/2
Step-by-step explanation:
Step 1: Write equation
-4(3/2x - 12) = -15
Step 2: Solve for <em>x</em>
- Distribute -4: -6x + 48 = -15
- Subtract 48 on both sides: -6x = -63
- Divide both sides by -6: x = 21/2
Answer: she is 60 years old because 48+12=60 yrs old now
Remember that a quadratic equation is a parabola. The equation is of the type y = Ax^2 + Bx + C
A linear equation is a straight line. The equation is of the type y = MX + N
The soluction of that system is Ax^2 + Bx + C = MX + N
=> Ax^2 + (B-M)x + (C-N) = 0
That is a quadratic equation.
A quadratic equation may have 0, 1 or 2 real solutions. Those are all the possibilitis.
So you must select 0, 1 and 2.
You can also get to that conclusion if you draw a parabola and figure out now many point of it you can intersect with a straight line.
You will realize that depending of the straight line position it can intersect the parabola in none point, or one point or two points.
