Let a0, b0, c0.Then both the roots of the equation ax2+bx+c=0.are.?

Question

Let a>0, b>0, c>0.Then both the roots of the equation ax2+bx+c=0.are.?

Answer

Just calculate b^2 -4ac but it will depend the value of these three constants a,b,c bcz your given information is not sufficient for us but it can surely be said that the curve of this equation must have the range from (-D/4a,infinity) it has a minimum point which is (-b/2a,D/4a)

Answer

Negative.sum of roots = -b/awhich is negative since b and a>0product of roots =c/2a which is positive since c,a>0so both the roots must be negative since product of two negatives is positive and sum of two negatives is negative.

Answer

Negative or complex root

Answer

Tell me its negative or positive..? Semma

Answer

As coefficient of a is positive and whole eq is positive it will have imajinary roots

Answer

Use sridharacharya

Answer

Introduction
The quadratic equation $ ax^2 + bx + c = 0 $ presents a significant inquiry into the nature of its roots, especially when the coefficients $ a $, $ b $, and $ c $ are all positive.
Discriminant Analysis
To determine the roots, we utilize the discriminant $ D $ from the quadratic formula $ x = \frac{-b \pm \sqrt{D}}{2a} $, where:

$ D = b^2 - 4ac $

Condition for Real Roots
For the roots to be real:

$ D \geq 0 $

Since $ a > 0 $, $ b > 0 $, and $ c > 0 $, we analyze $ b^2 - 4ac $:
- Given $ a, b, c > 0 $, $ D $ can be negative since $ 4ac $ can potentially exceed $ b^2 $.
Nature of Roots
1. If $ D > 0 $:
- The equation has two distinct real roots.
2. If $ D = 0 $:
- The equation has one real root (a repeated root).
3. If $ D < 0='' />:
- The equation has no real roots, indicating complex roots.
Given that \( 4ac $ often exceeds $ b^2 $ when $ a, b, c > 0 $, under typical conditions, we often find that:
Conclusion
Thus, unless specific values of $ a, b, $ and $ c $ are chosen such that $ b^2 \geq 4ac $, the roots of the equation $ ax^2 + bx + c = 0 $ will likely be complex. This highlights the importance of the relationship between $ b^2 $ and $ 4ac $ in determining the nature of the roots.

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