Question

If p(x) is a quadratic polynomial which is
divisible by (2x-1) and (x+1) and leaves
remainder 12 on division by x-1, then which
of the following are correct?
(a) The coefficient of x in p(x) is 6
(b) The constant term in p(x) is -6
(c) p(0)= P(1)
(d) p(x) is a perfect square
(e) None of these​

Answer 1

Answer:

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Answer 2

Given,

p(x) is divisible by (2x-1) and (x+1)

To find,

which of the given options is correct

Solution,

p(x) = k (2x-1)(x+1)

= 2kx^2 + kx - k

When this is divided by x-1 it gives 12 as remainder.

When we divide (2kx^2 + kx - k) by (x-1) we get the remainder 2k

Now, 2k = 12

which means k = 12/2

= 6

So the final equation will be 12x^2 + 6x - 6

So, the correct option is A - The constant term in p(x) is 6