Question

If a, b are zeros of polynomial 3x² - 7x - 6 find a polynomial whose zeros are a² and b²​

Answer 1

Answer:

let f(x)=3x²-7x-6

=>f(x)=3x²-9x+2x-6

=3x(x-3)+2(x-3)

=(x-3)(3x+2)

Let f(x)=0

=>(x-3)(3x+2)=0

=> x-3=0 , 3x+2=0

=> x=3 ,x= -2/3

given a,b are zeroes of f(x)

:.a=3 , b= -2/3

=>a²=9 , b²= 4/9

if a²,b² are zeroes of an unknown polynomial

=> p(x)=x²-(a²+b²)x+(a²)(b²)

=> p(x)=x²-(9+4/9)x+(9)(4/9)

=x²-85x/9+4