SOLUTION: sorry i don't have a book its on my computer...but the question is solve the following inequality for x. 19x^2+24x+1<0

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Question 32008: sorry i don't have a book its on my computer...but the question is solve the following inequality for x. 19x^2+24x+1<0
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
19x^2+24x+1<0
solve 19x^2+24x+1=0 using quadratic formula..let the 2 roots be a and b in increasing order.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-24+%2B-+sqrt%28+24%5E2-4%2A19%2A1+%29%29%2F%282%2A19%29+
x+=+%28-24+%2B-+sqrt%28+576-76+%29%29%2F%2838%29+
x+=+%28-24+%2B-+10%2Asqrt%285%29%29%2F38+%29
x+=+%28-24+%2B+10%2Asqrt%285%29%29%2F38+%29=b
x+=+%28-24+-+10%2Asqrt%285%29%29%2F38+%29=a
call the 2 roots a and b
now then this can be written as (x-a)(x-b)=0
if this product has to be not equal to 0 but less than zero,
then x should lie between a and b.,since then while one factor is positive the other would be negative and the product would be negative.