Question

If 1 and -1 are the zeroes of the polynomial p (x) = a^3 + x^2 − 2x + b , find the values of a and b.

Answer 1

sorry for so many cuttings..

Answer 2

Answer:

a = 2 , b = –1

Note:

★ If x = a is zero of any polynomial p(x) , then the polynomial becomes zero at x = a , ie; p(a) = 0 .

Solution:

Here,

The given polynomial is ;

p(x) = ax³ + x² - 2x + b

Also,

It is given that , x = ± 1 are the zeros of the given polynomial p(x) , thus p(±1) = 0 .

Thus,

=> p(1) = 0

=> a(1)³ + (1)² - 2(1) + b = 0

=> a + 1 - 2 + b = 0

=> a + b - 1 = 0

=> a = 1 - b ---------(1)

Also,

=> p(-1) = 0

=> a(-1)³ + (-1)² - 2(-1) + b = 0

=> -a + 1 + 2 + b = 0

=> -a + b + 3 = 0

=> a = b + 3 ---------(2)

From eq-(1) and (2) , we have ;

=> 1 - b = b + 3

=> - b - b = 3 - 1

=> -2b = 2

=> b = 2/-2

=> b = -1

Now,

Putting b = -1 in eq-(1) , we have ;

=> a = 1 - b

=> a = 1 - (-1)

=> a = 1 + 1

=> a = 2

Hence,

a = 2 , b = –1