Question

Find the value of b if ∝ and 1/∝ are zeroes of polynomial ax2+bx+c.

Answer 1

Answer:

hope it will help you....

Answer 2

Given data:

$\alpha$ and $\frac{1}{\alpha}$ are the zeroes of the polynomial $ax^{2}+bx+c$.

To find: the value of $b$

Step-by-step explanation:

The given polynomial is $ax^{2}+bx+c$

Since $\alpha$ and $\frac{1}{\alpha}$ are its zeroes, by the relation between zeroes and coefficients, we get

$\quad \alpha+\frac{1}{\alpha}=-\frac{b}{a}$

and $\alpha\times\frac{1}{\alpha}=\frac{c}{a}$

$\Rightarrow 1=\frac{c}{a}$

$\Rightarrow c=a$

Again since $\alpha$ is a zero of the given polynomial, we can write

$\quad a{\alpha}^{2}+b\alpha+c=0$

$\Rightarrow a{\alpha}^{2}+b\alpha+a=0$ since $c=a$

$\Rightarrow b\alpha=-(1+{\alpha}^{2})a$

$\Rightarrow \boxed{b=-\frac{1+{\alpha}^{2}}{\alpha}a}$

Answer: $b=-\frac{1+{\alpha}^{2}}{\alpha}a$