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