If the difference of the roots of the equation x^2+px+q=0 be unity , then (p^2+4q^2) equals to

Question

anonymous · Answer

(a) (1+2q)^2         (b)1-2q)^2
(c)4(p-q)^2           (d)2(p-q)^2

vishweshshrimali5 · Answer

$$\large{\alpha + \beta = -p}\tag{1}$$

$$\large{\alpha \beta = q}\tag{2}$$

$$\large{\alpha - \beta = 1}\tag{3}$$

vishweshshrimali5 · Answer

Here I am assuming that the roots are alpha and beta

vishweshshrimali5 · Answer

Now using equations 1, 2 and 3:

$$\large{(\alpha + \beta)^2 = (\alpha-\beta)^2 + 4\alpha\beta}$$

$$\large{\implies p^2 = 1 + 4q}$$

vishweshshrimali5 · Answer

Well appears the this equation is not useful for now ;)

ganeshie8 · Answer

option a satisfies above equation :P

vishweshshrimali5 · Answer

^^^ Perfect method :P

ganeshie8 · Answer

weird way to cook up options lol

vishweshshrimali5 · Answer

Lol :D

vishweshshrimali5 · Answer

(a) (1+2q)^2 = 1 + 4q^2 + 4q = p^ + 4q^2

vishweshshrimali5 · Answer

GOT IT !!!! :P

anonymous · Answer

wait a min

vishweshshrimali5 · Answer

Solve the option a and use this equation:

$\color{blue}{\text{Originally Posted by}}$ @vishweshshrimali5
Now using equations 1, 2 and 3:

$$\large{(\alpha + \beta)^2 = (\alpha-\beta)^2 + 4\alpha\beta}$$

$$\large{\implies p^2 = 1 + 4q}$$
$\color{blue}{\text{End of Quote}}$


You will get the answer

anonymous · Answer

yes got

vishweshshrimali5 · Answer

Great :D