Question

if a,b are the roots of x^2-x+2, then a^2b+ab^2 is
I will mark as brainliest
Please don't spam or I will report you ​

Answer 1

(x+a)(x+b) = 0

x^2 +(a+b)x +ab = 0

Comparing with x^2 + 2x + 2 = 0

a + b = 2

ab = 2

(a-b)^2 = (a+b)^2 - 4ab = 4 - 8 = -4 = i^2×2^2

a-b = i2

2a = 2+i2 or a = 1 + I

b =1 - I Now a^15 = (1+I)^15

b^15 = (1 - I)^15

a^15 = (1 + I)(1 + I)^2×7= (1+I)(1+2i+i^2)^7

a^15 =(1+I)(i2)7= (1+I)(I)7(2)^7 = 128(I)(I)^2×3(1+I)

a^15 = 128(-i)(1+I) = 128(-i -i^2) = 128(1-i)

Similarly b^15 = 128(1+I)

a^15 +b^15 =128 - 128i +128+128i = 256*

a^15 + b^15 = 256

Answer 2

Answer:

if a,b are the roots of x^2-x+2, then a^2b+ab^2 is

I will mark as brainliest