Question

1 mark question from quadratic equations​

Answer 1

❏ Question:-

@ if the equation

if the equation (m²+n²)x²-2(mp+nq)+(p²+q²) ; has equal roots then ,

1) mp=nq

2)mq=np

3)mn=pq

4)mq=$\sqrt{np}$

❏ Solution:-

We know that for the quadratic equation.

ax²+bx+c = 0

the roots will be , equal if

$\sf \boxed{b^2-4ac= 0}$

Now,

(m²+n²)x²-2(mp+nq)+(p²+q²) =0 ; comparing this with the equation , ax²+bx+c=0 , we get.

a=(m²+n²)

b=-2(mp+nq)

c= p²+q²

now applying the condition we get,

➩b²=4ac

➩[-2(mp+nq)]²=4(m²+n²)(p²+q²)

➩4(m²p²+n²q²+2mnpq)=4(m²p²+m²q²+n²p²

+n²q²)

➩m²p²+n²q²+2mnpq=m²p²+m²q²+n²p²+n²q²

➩2mnpq=m²q²+n²p²

➩m²q²-2(ma)(np)+n²p²=0

➩(mq-np)²=0

➩mq-np=0

➩mq=np

Option ➩ (2) mq=np