Question

If the sum and product of two zeroes of the polynomial x3+x2-3x-3 are 0 and 3 respectively , find all zeroes of the polynomial. ​

Answer 1

Answer:

Two zeros of p(x) are √3 and -√3.

Step-by-step explanation:

I'm writing aplha as @ and beta as ß, so don't get confused.

Let @ and ß be the zeros of P(x)

P(x)= x³+x²-3x-3

Given,

Sum of zeros= @+ß= 0

Product of zeros= @*ß= 3

@+ß=0

=@= -ß

Put @= -ß in @*ß=3

=> -ß*ß=3

=> -ß²=3

=> -ß=√3

=> ß= -√3

Again,

@+ß=0

=>@+(-√3)=0

=>@= √3

Therefore, @=√3 and ß= -√3.

Hence, two zeros of p(x) are √3 and -√3.

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Answer 2

Answer:

Step-by-step explanation:

x^2 - 2x - x + 2

x(x - 2) - 1(x-2) = 0

(x-1)(x-2) = 0

x= 1 , 2

sum of zeroes = a +b = -b/a

= 1 + 2 = 3 = -(-3/1) = 3

product of zeroes = ab = c/a

= 1 x 2 = 2 = 2/1 = 2