Question

IF P AND Q ARE THE ROOTS OF THE EQUATION X2 -3X +2 = 0 THEN FIND THE Value of 1/p-1/q

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\frac{1}{p}-\frac{1}{q}=\pm \frac{1}{2}$

Step-by-step explanation:

Given : If p and q are the roots of the equation $x^2-3x +2 =0$.

To find : The value of $\frac{1}{p}-\frac{1}{q}$ ?

Solution :

In equation $x^2-3x +2 =0$

Here, a=1, b=-3 and c=2.

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

$p+q=-\frac{-3}{1}$

$p+q=3$

The product of roots $pq=\frac{c}{a}$

$pq=\frac{2}{1}$

$pq=2$

The value of $\frac{1}{p}-\frac{1}{q}$

$\frac{1}{p}-\frac{1}{q}=\frac{q-p}{pq}$

Squaring both side,

$(\frac{1}{p}-\frac{1}{q})^2=\frac{(q-p)^2}{(pq)^2}$

$(\frac{1}{p}-\frac{1}{q})^2=\frac{(q+p)^2-4pq}{(pq)^2}$

Substitute the value,

$(\frac{1}{p}-\frac{1}{q})^2=\frac{(3)^2-4(2)}{(2)^2}$

$(\frac{1}{p}-\frac{1}{q})^2=\frac{9-8}{4}$

$(\frac{1}{p}-\frac{1}{q})^2=\frac{1}{4}$

Taking root both side,

$\frac{1}{p}-\frac{1}{q}=\pm \frac{1}{2}$

#Learn more

In the quadratic equation ax2 + bx + c = 0, if the sum of the roots is equal to the product of the roots, find the sum of the reciprocals of the roots.

brainly.in/question/11200939