Question

6.
If the zeros of the polynomial x°- 3x +x+1 are a - b, a, a + b then find 'a' and b.
በ Ir a Barcere​

Answer 1

Given :-$f(x)=x^{3} -3 x^{2} +x+1$

are a-b = α ------ 1

a =β

a + b = ω

$a+\beta+\gamma=\frac{-(-3)}{1}=3$

$\begin{array}{r}a-1+a+a+y=3 \\3 a=3 \Rightarrow1\end{array}$$As we know that coeificent of x or x^{3} is 1$$Therefore \alpha \beta+\beta \gamma+\gamma \alpha=1$

As we know that from equation  1

$(a-b) a+a(a+b)+(a+b)(a-b)=1$

$a^{2}-a b+a^{2}+a b+a^{2}-b^{2}=1\\3 a^{2}-b^{2}=1 as we put a = 1$

$b^{2}=2 \Rightarrow b=\pm \sqrt{2}$

Hence a = 1 and $b=\pm \sqrt{2}$