Question

The absolute difference between
the integral values of P such
that(x-p)(x-12)+2 = 0 has integral roots is​

Answer 1

Step-by-step explanation:

Given:

$(x - p)(x - 12) + 2 = 0$

To find:Find absolute difference between

the integral values of P such that the quadratic equation has integer roots.

Solution:

Step 1: Write the equation by taking 2 to other side

$(x - p)(x - 12) = - 2$

Step 2: Multiplication of two factors will be -2 for the values(Integer values)

case1: (-2)(1) = -2

case2:(2)(-1) = -2

case3:(1)(-2)= -2

case 4: (-1)(2)= -2

Step 3: Put the value of case 1 and solve x then p

$x - 12 = 1 \\ \\ x = 13 \\ \\ so \\ \\ 13 - p = - 2 \\ \\ - p = - 15 \\ \\ p = 15$

Step 4:Put the value of case 2 and solve x then p

$x - 12 = - 1 \\ \\ x = 11 \\ \\ so \\ \\ 11 - p = 2 \\ \\ - p = - 9\\ \\ p = 9$

Step 5: Put the value of case 3 and solve x then p

$x - 12 = - 2 \\ \\ x = 10 \\ \\ 10 - p = 1 \\ \\ p = 9$

Step 6: Put the value of case 4 and solve x then p

$x - 12 = 2 \\ \\ x = 14 \\ \\ thus \\ \\ 14 - p = - 1 \\ \\ p = 15$

Final Answer: The absolute difference between the integral value of p is 6 because value of p must be either 9 or 15, so that the given quadratic equations has integer roots.

Hope it helps you.

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