Q. 23.7( 6 Votes )
If a, b, c 
R, a > 0, c < 0, then prove that the roots of ax2 + bx + c = 0 are real and distinct.
Answer :
For roots to be real and distinct D should be greater than 0
Discriminant (D) = b2 – 4ac
In the discriminant b2 is a positive number since square cannot be negative given a > 0 which means a is also positive
Now consider the product – 4 × c
As c < 0 c is negative
We are multiplying two negative numbers which would result in a positive number which means – 4 × c is also positive
So, we can conclude that b2 – 4ac is positive
Hence D > 0
Hence roots are real and distinct
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