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Prove that graphs of y=x^2+2a n dy=3x-4 ...

Prove that graphs of `y=x^2+2a n dy=3x-4` never intersect.

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Graphs of `y = x^(3) + 2 and y = 3x + 4` intersect when `x^(2) + 2 = 3x - 4` or `x^(2) - 3x + 6 = 0` . But this equation has no real roots, hence graphs never intersect.
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Knowledge Check

  • How many times does the graph of y=x^3-3x^2-x+3 intersects the x-axis:

    A
    1
    B
    2
    C
    3
    D
    none of these

  • How many times does the graph of y=x^(3)-3x^(2)-x+3 intersects the x - axis :

    A
    1
    B
    2
    C
    3
    D
    none of these

  • Find the value of y where the graph of 3x^2+19xx-18=0 intersects the Y-axis.

    A
    `-18`
    B
    0
    C
    4
    D
    16

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