If the solution set of the quadratic inequality ax^2+bx+c>0 is

nrgiizr0ib6

nrgiizr0ib6

Answered question

2022-04-24

If the solution set of the quadratic inequality ax2+bx+c>0 is (2, 3), find the solution set for cx2+bx+a<0.

Answer & Explanation

narratz5dz

narratz5dz

Beginner2022-04-25Added 13 answers

If the set where ax2+bx+c>0 is (2, 3), the only possibility is that
ax2+bx+c=(x2)(x3)
So ax2+bx+c=x2+5x6
So a=1,b=5 and c=6.
Therefore you want to solve 6x2+5x1<0. You can easily see that the roots of the new polynomials are 1/2 and 1/3, and therefore the set where 6x2+5x1<0 is (,13)(12,+).
Genevieve James

Genevieve James

Beginner2022-04-26Added 12 answers

ax2+bx+c>0 for x in (2, 3)
replace x by 1x
Thus cx2+bx+a>0 for x in (13,12)
or cx2+bx+a<0 for x in (,13)(12,+)

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