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Q: What are the possible values of k in the line y equals kx -2 which is tangent to the curve of y equals x squared -8x plus 7?

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The possible values for k are -2 and -14 because in order for the line to be tangent to the curve the discriminant must be equal to 0 as follows:- -2x-2 = x2-8x+7 => 6-x2-9 = 0 -14x-2 = x2-8x+7 => -6-x2-9 = 0 Discriminant: 62-4*-1*-9 = 0

(x, y) = (-3, -3) or (3, 3)

-2

If: y = x-4 and y = x2+y2 = 8 then 2x2-8x+8 = 0 and the 3 ways of proof are: 1 Plot the given values on a graph and the line will touch the curve at one point 2 The discriminant of b2-4ac of 2x2-8x+8 must equal 0 3 Solving the equation gives x = 2 or x = 2 meaning the line is tangent to the curve

The gradient to the curve y = x2 - 8x + 7 is dy/dx = 2x - 8The gradient of the tangent to the curve is, therefore, 2x - 8.The gradient of the given line is kTherefore k = 2x - 8. That is, k can have ANY value whatsoever.Another Answer:-If: y = kx-2 and y = x2-8x+7Then: x2-8x+7 = kx-2 => x2-8x-kx+9 = 0Use the discriminant of: b2-4ac = 0So: (-8-k)2-4*1*9 = 0Which is: (-8-k)(-8-k)-36 = 0 => k2+16k+28 = 0Using the quadratic equation formula: k = -2 or k = -14 which are the possible values of k for the straight line to be tangent with the curve

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The possible values for k are -2 and -14 because in order for the line to be tangent to the curve the discriminant must be equal to 0 as follows:- -2x-2 = x2-8x+7 => 6-x2-9 = 0 -14x-2 = x2-8x+7 => -6-x2-9 = 0 Discriminant: 62-4*-1*-9 = 0

Using the discriminant the possible values of k are -9 or 9

If: y = kx -2 and y = x^2 -8x+7 Then the values of k work out as -2 and -14 Note that the line makes contact with the curve in a positive direction or a negative direction depending on what value is used for k.

(x, y) = (-3, -3) or (3, 3)

-2

If the line y = kx - 2 is a tangent to the curve y = x² - 8x + 7, then where they meet: kx - 2 = x² - 8x + 7 → x² - (8+k)x + 9 = 0 will have a repeated root, ie the determinant is zero: (8+k)² - 4 ×1 × 9 = 0 → 64 + 16k + k² - 36 = 0 → k² + 16k + 28 = 0 → (k + 2)(k + 14) = 0 → k = -2 or -14.

If: y = x-4 and y = x2+y2 = 8 then 2x2-8x+8 = 0 and the 3 ways of proof are: 1 Plot the given values on a graph and the line will touch the curve at one point 2 The discriminant of b2-4ac of 2x2-8x+8 must equal 0 3 Solving the equation gives x = 2 or x = 2 meaning the line is tangent to the curve

If you mean "are there two values which, when squared, equal 100" then the answer is yes. 102 = 100 -102 =100 If you mean "Can 1002 result in two different answers" then the answer is no. 1002 = 10,000

4,3,2,1,0

The gradient to the curve y = x2 - 8x + 7 is dy/dx = 2x - 8The gradient of the tangent to the curve is, therefore, 2x - 8.The gradient of the given line is kTherefore k = 2x - 8. That is, k can have ANY value whatsoever.Another Answer:-If: y = kx-2 and y = x2-8x+7Then: x2-8x+7 = kx-2 => x2-8x-kx+9 = 0Use the discriminant of: b2-4ac = 0So: (-8-k)2-4*1*9 = 0Which is: (-8-k)(-8-k)-36 = 0 => k2+16k+28 = 0Using the quadratic equation formula: k = -2 or k = -14 which are the possible values of k for the straight line to be tangent with the curve

Since the word 'equals' appears in your questions it might be what is called a trigonometric identity, in other words a statement about a relationship between various trigonometric values.

If y = cx + 1 is a tangent then it intersects the curve only once. Therefore cx + 1 = 3x^2 - 4x + 4 has only one root that is, 3x^2 - (c+4)x + 3 has a single root therefore the discriminant is 0: (c+4)^2 - 4*3*3 = 0 (c+4)^2 = 36 c + 4 = sqrt(36) = -6 or +6 Therefore c = -10 or c = 2.