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find the condition that px^(3) + qx^(2)...

find the condition that ` px^(3) + qx^(2) +rx +s=0` has exactly one real roots, where `p ,q ,r,s,in R`

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To find the condition under which the cubic polynomial \( px^3 + qx^2 + rx + s = 0 \) has exactly one real root, we can follow these steps: ### Step 1: Understanding the Roots of the Polynomial A cubic polynomial can have either: - Three real roots, or - One real root and two complex (imaginary) roots. Since we need the condition for exactly one real root, it implies that the other two roots must be complex. ...
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