Answered

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The line y = 2x – 3 touches the curve y = x^2 + kx + 6. Find the possible values of k.

Sagot :

abidemiokin

The value of "k" will be a value greater than 4 or less than -8

If the line y = 2x – 3 touches the curve y = x^2 + kx + 6, this means that both equations will be equal as shown:

[tex]2x - 3 = x^2 + kx + 6[/tex]

Rewrite in the form [tex]ax^2+bx+c=0[/tex]

[tex]2x - 3 = x^2 + kx + 6\\x^2+kx-2x+6+3 =0\\x^2+(k-2)x+9=0\\[/tex]

The roots has a distinct solution if b² - 4ac > 0

From the equation

a = 1

b = k-2

c = 9

Substitute into the formula:

[tex](k-2)^2-4(1)(9) > 0\\k^2-4k+4-36>0\\k^2-4k-32>0[/tex]

Factorize

[tex]k^2+8k-4k-32 >0\\k(k+8)-4(k+8)>0\\(k-4)(k+8)>0\\k>4 and k>-8[/tex]

Hence the value of "k" will be value greater than 4 or less than -8

Learn more here: https://brainly.com/question/24896483

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