Question

find the value of p when px^2+(root 3-root 2)x-1=0 and x=1/root 3 is one root of this equation

Answer 1

Answer:

the value of p is 3√6

Step-by-step explanation:

Given equation is : px² + (√3 - √2)x - 1 = 0

if x = $\frac{1}{\sqrt{3} }$

We are given one root of the equation.

This means that this root will satisfy the given equation.

Therefore, substituting the value in the given equation.

=> p($\frac{1}{\sqrt{3} }$)² + (√3 - √2)($\frac{1}{\sqrt{3} }$) - 1 = 0

=> p/3 + (1 - √2/√3) - 1 = 0

=> p/3 - √6 = 0

=> p/3 = √6

=> p = 3√6

Therefore, the value of p is 3√6