Question

Solve this.....


Class 10th prob...

Need soln.​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

Let a, b, c, d be distinct integers such that the equation (x - a)(x - b)(x - c)(x - d) - 9 = 0 has an integer root r, then the value of (a+b+c+d - 4r) is equal to ?

Sᴏʟᴜᴛɪᴏɴ :-

→ (x - a)(x - b)(x - c)(x - d) - 9 = 0

→ (x - a)(x - b)(x - c)(x - d) = 9

Now , Given That, r is a root of the given Equation,

So,

→ (r - a)(r - b)(r - c)(r - d) = 9

Splitting RHS part Now, we get,

→ (r - a)(r - b)(r - c)(r - d) = 3 * 1 * (-3) * (-1)

Comparing Now, we get,

→ r - a = 3

→ a = (r - 3)

And,

→ r - b = 1

→ b = (r - 1)

And,

→ r - c = (-3)

→ c = (r + 3)

And,

→ r - d = (-1)

→ d = (r + 1) .

To Find :- (a+b+c+d - 4r)

→ (a+b+c+d - 4r)

Putting values of a,b,c & d now,

→ (r - 3) + (r - 1) + (r + 3) + (r + 1) - 4r

→ 4r - 4 + 4 - 4r

→ (4r - 4r) + (4 - 4)

→ 0 + 0

→ 0 (Ans.)