Q10 of 25 Page 2

On dividing p(x) = x4 – 3ax2 + 1 by (x – 2), we get a remainder 3. Find the value of a.

To Find: a


Given: p(x) = x4 – 3ax2 – 1 is divided by (x – 2)


Concept Used:


If a polynomial p(x) is divided by (x – k), then p(k) is the remainder we get when p(x) will be divided by (x – k)


Explanation:


P(2) = (2)4 – 3a(2)2 – 1


P(2) = 16 – 12a – 1


P(2) = 3


Therefore,


16 – 12a – 1 = 3


15 – 12a = 3


–12a = 3 – 15


–12a = –12


a = 1


Hence, the value of a is 1.


More from this chapter

All 25 →
8

Find a cubic polynomial whose zeroes are 3, 1/2, and –1.

 9

What should be added to the polynomial x2 – 5x + 4, so that 3 is the zero of the resulting polynomial?

 11

Find the zeroes of the quadratic polynomial p(x) = 6x2 – 3 – 7x. And also, verify the relationship between zeroes and coefficient.

 12

If α and β are the zeros of the quadratic polynomial p(x) = 4x2 – 5x – 1, find the value of α2β + αβ2