Question

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

Answer 1

Answer:

p(x) = ax³+x²-2x+b

1 and –1 are zeroes of p(x)

Now,

p(1) = a(1)³+(1)²-2(1)+b

0 = a + 1 - 2 + b

1 = a + b ............... (1)

p(-1) = a(-1)³+(-1)²-2(-1)+b

0 = -a +1 + 2 + b

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

Add eq (1) and (2),

2b = -2

b = -1

put in (1),

a = 1 – b

a = 1 – (-1)= 2

Thus,

value of a = 2 and b = -1

Answer 2

Step-by-step explanation:

If 1 and -1 are the factors of p(x) the according to factors theorem, p(-1) and p(1) must be zero

Now, p(-1) = a(-1)³ + (-1)² - 2X(-1) + b

= p(-1) = -a + 1 + 2 + b

= p(-1) = 3-a +b

now, 3-a + b = 0. according to factors theorem

= -a + b = -3

= -(a-b) = -3

= a-b = 3 ......(i)

And, p(1) = a(1)³ + (1)² - 2(1) + b

= p(1) = a+1-2+b

= p(1) = a+b-1

= a+b-1 = 0

= a+b = 1. .......(ii)

On subtracting (i) and (ii), we get=

= -2b = 2

so b = -1

then a = 2 (as a-b = 3 )

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