x^3-kx^2+x+2 and x^2-x-2 have two common zeroes then 1-k=
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The maximum number of zeros that a quadratic equation can have is two zeros.
Hence, it is given that it has 2 common zeros. So, the 2 zeros of the equation are the common zeros for both of them.
Given equation:
- x³ - kx² + x + 2 = 0
- x² - x - 2 = 0
Solving equation 2, we get,
⇒ x² - 2x + x - 2 = 0
⇒ x ( x - 2 ) + 1 ( x - 2 ) = 0
⇒ ( x + 1 ) ( x - 2 ) = 0
⇒ x = -1, 2
Hence the common two zeros are -1 and 2.
Substituting the zeros in the first equation we get,
⇒ x³ - kx² + x + 2 = 0
⇒ 2³ - k ( 2 )² + 2 + 2 = 0
⇒ 8 - 4k + 4 = 0
⇒ 12 = 4k
⇒ k = 12/4 = 3
Hence the value of 'k' is 3.
⇒ 1 - k = 1 - 3 = -2.
Hence -2 is the answer !!
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