Question

If p and q are the zeroes of the polynomial 3x-5x+2 write the polynomial in"x"whose zeroes are 1/p and 1/q

Answer 1

Answer:

hope that it will helps you dear

Answer 2

The polynomial in"x"whose zeroes are $\frac{1}{p}$ and $\frac{1}{q}is x^{2} -(\dfrac{5}{2} )x+\dfrac{3}{2}.$

Explanation:

The given quadratic equation is:

$3x^{2} -5x+2$

p and q are the zeroes of the $3x^{2} -5x+2$.

We know that,

The sum of the roots, $p+q= \frac{-b}{a}$

⇒ $p + q= \frac{5}{3}$

And, the product of the roots, $pq= \frac{c}{a}$

⇒$pq= \frac{2}{3}$

The polynomial in"x"whose zeroes are $\frac{1}{p}$ and $\frac{1}{q}$

= $x^{2} -(\dfrac{1}{p}+\dfrac{1}{q})x+\dfrac{1}{p}\dfrac{1}{q}$

$= x^{2} -(\dfrac{5}{3}\dfrac{3}{2}  )x+\dfrac{3}{2}$

$= x^{2} -(\dfrac{5}{2} )x+\dfrac{3}{2}$

Hence, the polynomial in"x"whose zeroes are $\frac{1}{p}$ and $\frac{1}{q}$ is $x^{2} -(\dfrac{5}{2} )x+\dfrac{3}{2}$.