Question

If p and q are the roots of the quadratic equation (1 + √2)x² – (√5 + √10)x + (1 + √2) = 0, then, the value of (p – q) is – 

1. -2
2. 2
3. 1
4. 3

Answer 1

Correct Answer - Option 3 : 1

Given:

(1 + √2)x² – (√5 + √10)x + (1 + √2)

Roots of equation: p and q

Concept Used:

If a quadratic equation (ax² + bx + c=0)

Then, p + q = - b/a and pq = c/a

Calculation:

(1 + √2)x² – (√5 + √10)x + (1 + √2)

p + q = - (- √5 - √10)/(1 + √2) = √5 [ 1 + √2]/(1 + √2) = √5

pq = (1+ √2)/(1 + √2)= 1

So, (p + q) = √5 and pq = 1

Now, (p – q) = √[(p + q)² – 4pq]

⇒ √[(√5)² – 4(1)]

⇒ √(5 – 4)

⇒ 1