Location of Roots in Quadratic EquationWe learnt about the location of roots of quadratic equation in class today. I have a problem in one case specifically, the one where both the roots are required in the interval ( k 1 , k 2 ) where k 1 , k 2 are real constant numbers. So the conditions given to us were,1. Δ greater than or equal to 0 (fairly obvious)2. a f ( k 1 ) &gt; 0 where f ( k 1 ) is the value of the function at k 1 and a is the leading coefficient3. a f ( k 2 ) &gt; 0 (both of these are again understandable)4. then comes k 1 &lt; − b / 2 a &lt; k 2 i.e. the abscissa of the vertex of the parabola lies in the interval required.

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Location of Roots in Quadratic EquationWe learnt about the location of roots of quadratic equation in class today. I have a problem in one case specifically, the one where both the roots are required in the interval   (      k    1    ,      k    2    ) where       k    1    ,      k    2   are real constant numbers. So the conditions given to us were,1.   Δ greater than or equal to 0 (fairly obvious)2.   a  f  (      k    1    )  &amp;gt;  0 where   f  (      k    1    ) is the value of the function at       k    1   and a is the leading coefficient3.   a  f  (      k    2    )  &amp;gt;  0 (both of these are again understandable)4. then comes       k    1    &amp;lt;  −  b      /    2  a  &amp;lt;      k    2   i.e. the abscissa of the vertex of the parabola lies in the interval required.

gortepap6yb · Accepted Answer

Explanation:You&#039;re missing an essential point: conditions 2 and 3 mean that       k    1   and       k    2   are outside the interval of the roots. However, they might be on the same side of this interval.Step 2Therefore, supposing conditions 2 and 3 is not enough, we must add the condition that       k    1    ,      k    2   are not on the same side, which is equivalent to their arithmetic mean being in the interval   (      k    1    ,      k    2    ).

Location of Roots in Quadratic Equation. We learnt about the location of roots of quadratic equation in class today. I have a problem in one case specifically, the one where both the roots are required in the interval (k_1, k_2) where k_1, k_2 are real constant numbers.

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