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ELEN [110]
3 years ago
9

Please help me with this!

Mathematics
1 answer:
stich3 [128]3 years ago
7 0

Answer:

y = x^2 - 4x - 6.

Step-by-step explanation:

The roots are  2 + √10 and 2 - √10, so in factor form we have:

(x -  (2 + √10))(x - (2 - √10))

= ( x -  2 - √10)(x - 2 + √10)

= x^2 - 2x + √10x - 2x + 4 - 2√10 - √10x  + 2√10 - √100

=  x^2 -4x + 4 - 10

= x^2 - 4x - 6.

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You need to find points where the line g(x) intercepts the quadratic function f(x) in one and only one point.

Then 3x^2 + 4x -2 = mx - 5

solve 3x^2 + 4x - mx -2 + 5 = 0

3x^2 + (4 - m)x + 3 = 0

In order to there be only one solution (one intersection point) the radicand of the quadratic formula must be 0 =>

b^2 - 4ac = (4 - m)^2 - 4(3)(3) = 0

(4 - m)^2 = 24

4 - m = +/- √(24)

m = 4 +/- √(24) = 4 +/- 2√(6)

Then m, the slope of the line, may be 4 + 2√6 and 4 - 2√6




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