Question

if p and q are roots of equation x^2 +pq -q =0 , then find p and q​

Answer 1

Correct Question :-

If p and q are roots of equation x^2 + px + q = 0 then find p and q

[ Reason, It is a quadratic equation and we always write quadratic equation ax^2+bx + c and here p and q are the roots and we cannot write pq together ]

Solution :-

Given that, p and q are the roots of equation

x^2 + px - q = 0

Compare this equation with quadratic equation

ax^2 + bx + c =0

[ Quadratic equation is a equation which has highest power of degree 2 ]

Therefore,

a = 1 , b = p, c = q

Now,

Sum of roots = -b/a

p + q = -p/1

1( p + q) = -p

p + q = -p

q = -p -p

q = -2p. ( 1 )

Now,

Products of roots = c/a

pq = q/1

p * q = q/1

p * q = q

p = q/q

p = 1

Thus, The value of p = 1

From ( 1 )

q = -2 * 1 = -2

Hence, The value of p and q is 1 and -2$.$

Answer 2

Answer:

$\huge \mathfrak \red{Question}$

If p and q are roots of equation x^2 + px + q = 0 then find p and q

[ Reason, It is a quadratic equation and we always write quadratic equation ax^2+bx + c and here p and q are the roots and we cannot write pq together ]

$\huge \mathfrak \purple{Solution}$

Given that, p and q are the roots of equation

x^2 + px - q = 0

Compare this equation with quadratic equation

ax^2 + bx + c =0

[ Quadratic equation is a equation which has highest power of degree 2 ]

Therefore,

a = 1 , b = p, c = q

Now,

Sum of roots = -b/a

p + q = -p/1

1( p + q) = -p

p + q = -p

q = -p -p

q = -2p. ( 1 )

Now,

Products of roots = c/a

pq = q/1

p * q = q/1

p * q = q

p = q/q

p = 1

Thus, The value of p = 1

From ( 1 )

q = -2 * 1 = -2

▶Hence, The value of p and q is 1 and -2.