Question

if px2+3x+q=0 has two roots x=-1 and x=-2, find p-q

Answer 1

Answer:

The value of p-q is -1

Step-by-step explanation:

Concept:

If $\alpha\:and\:\beta$ are roots of $ax^2+bx+c=0$ then

sum of roots$=\alpha+\beta=\frac{-b}{a}$

product of roots$=\alpha.\beta=\frac{c}{a}$

Given equation is

px^2+3x+q=0

Here, a=p, b=3, c=q

sum of roots=$\frac{-b}{a}$

$(-1)+(-2)=\frac{-3}{p}\\\\-3=\frac{-3}{p}\\\\p=\frac{-3}{-3}\\\\p=1$

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

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

Now,

p - q = 1 - 2 = -1

Answer 2

Answer:

The value of p-q is -1

Step-by-step explanation:

Concept:

If alpha and beta are roots of  then

sum of roots are -1 and -3

product of roots

Given equation is

px^2+3x+q=0

Here, a=p, b=3, c=q

sum of roots=

product of roots=

Now,

p - q = 1 - 2 = -1