Question

If difference of roots of the equation x² - px +q=0 is 1, then p² +4q² equal​

Answer 1

Answer:

$difference \: \: of \: \: roots \: \: = \frac{ \sqrt{d} }{a} = 1 \\ \\ \frac{ \sqrt{ {p}^{2} - 4q} }{1} = 1 \\ \\ {p}^{2} - 4q = 1 \\ \\ {p}^{2} = 4q + 1 \\ \\ {p}^{2} + 4 {q}^{2} = {(4q + 1)}^{2} + 4 {q}^{2}$

Answer 2

Answer:

(2p + 1 )²

Step-by-step explanation:

roots are m , n

m+n = p , mn = p

m-n = 1

m²+n² = 1+2mn

p² +4q² = (m+n)² + 4m²n²  = 4m²n² + 4mn +1 = (2 mn +1 )² =  (2p + 1 )²