Question

Show that, the roots of the equation:-

(p²-q)x²+5(p+q)x-2(p-q) = 0

are real and distinct

class :- 10th
chapter :- quadratic equations

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Answer 1

Answer:

(p−q)x

2

+5(p+q)x−2(p−q)=0

Here, a=p−q,b=5(p+q),c=−2(p−q)

⇒ Discriminant=b

2

−4ac

=[5(p+q)]

2

−4(p−q)(p−q)

=25(p+q)

2

+8(p−q)

2

⇒ (p+q)

2

and (p−q)

2

are perfect squares and their values will always be greater than 0. As p



=q

∴ Discriminant>0

Hence, roots of the equation will be real an unequal.

Step-by-step explanation:

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Answer 2

Answer:

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