Question

If alpha and beta are the zeroes of the polynomial x2-5x+6, then find the polynom ial whose zeroes are 1/alpha and 1/beta .

Answer 1

here is your answer ..
hope this helps you....

Answer 2

Answer: The polynomial is,

$6x^2-5x+1$

Step-by-step explanation:

If $p$ and $q$ are the roots of a quadratic equation,

Then the quadratic equation is,

$x^2-(p+q)x+pq=0$

Here, the given quadratic equation is,

$x^2-5x+6$

Which having the zeroes, $\alpha$ and $\beta$.

For finding the zeroes,

$x^2-5x+6=0$

$x^2-3x-2x+6=0$

$x(x-3)-2(x-3)=0$

$(x-2)(x-3)=0$

Thus, the zeroes of the given quadratic equation are 2 and 3,

$\implies \alpha = 2\text{ and } \beta = 3$

$\implies \frac{1}{\alpha} = \frac{1}{2}\text{ and } \frac{1}{\beta}= \frac{1}{3}$

Hence, the required quadratic equation which having zeroes $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is,

$x^2-(\frac{1}{2}+\frac{1}{3})x+\frac{1}{2}\times \frac{1}{3}=0$

$\implies 6x^2-5x+1=0$