Question

The equations x² - 4x + k = 0 and x² + kx - 4 = 0, where k is a real number, have exactly one common root. What is the value of k?
See the answer is 03.
I just want detailed solution...
10 points.....

Answer 1

Subtract the 2nd equation from the first equation. Eliminate x^2 term.
Let x be the common root.

We get. - (k+4) x + k+4 = 0
x = 1 clearly.

Substitute x = 1 in the first equation to get. 1- 4 + k = 0
k = 3.

Answer 2

Hello
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x²-4x+k=0.................1
x²+kx-4=0....................2

solving 1&2

x²-4x+k=0
x²+kx-4=0
-   -   +
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(-4k)x+4k=0
∴x=1

substitute in eqn 1

x²-4x+k=0
1-4+k=0
-3+k=0
k=3

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hope it's help u