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3x2 + 4x + 1 = ??
This is a quadratic equation. The equation can be made to equal any number and this will determine the corresponding values of x.
EXAMPLE : 3x2 + 4x + 1 = 96 (x = 5 or x = -19/3)
Alternatively, if x is known then this will determine the result.
EXAMPLE : If x = 2 then (3 x 4) + (4 x 2) + 1 = 12 + 8 + 1 = 21
In normal use, a quadratic equation is presented as equal to zero.
In this example : 3x2 + 4x + 1 = 0
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Find the sum 3x2 plus 2x plus 3 plus x2 plus x plus 1?
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
Find the solutions for 4x squared plus 4x plus 1 equals 0?
x = -½
What is 3x plus 5 equals 4x plus 1?
If: 3x+5 = 4x+1 Then: x = 4
How would you work out the possible values of k in the line y equals kx plus 1 which is tangent to the curve of y equals 3x squared -4x plus 4?
If: y = kx+1 and y = 3x2-4x+4 Then: 3x2-4x+4 = kx+1 So: 3x2-4x-kx+3 = 0 For the line to be tangent to the curve the discriminant of b2-4ac must = 0 So when: -4*3*3 = -36 then (-4-k)2 must = 36 So it follows: (-4-k)(-4-k) = 36 => k2+8k-20 = 0 Solving the quadratic equation: k = 2 or k = -10
4x plus 6y equals 14 -2x plus 2y equals -2?
(2, 1)
