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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.

Text Solution

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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

  • Find the points at which the graphs of y=1/2x^2 -3 and y=x +1 intersect.

    A
    (-2,-3) (4,5)
    B
    (-1,-2) (5,4)
    C
    (-4,-3) (-2,4)
    D
    (-2,-1) (4,5)

  • The graphs of y=2x-5 and x + 3y=-1 intersect at

    A
    (-1,2)
    B
    (-2,-1)
    C
    (2,-1)
    D
    (-2,1)

  • If the graphs of x^(2) = 4(y+9) and x + ky = 6 intersect on the x-axis , then k =

    A
    0
    B
    6
    C
    `-6`
    D
    any real number