Question

x^3-kx^2+x+2 and x^2-x-2 have two common zeroes then 1-k=

Answer 1

Answer:

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 !!