Class 11Mathematics2 Complex Numbers and Quadratic Equations: Quadratic EquationsQuadratic expressions and Position of roots
DifficultIf $ax^2 + bx + c < 0$ for all $x \in R$ and the expressions $cx^2 + ax + b$ and $ax^2 + bx + c$ have their extreme values at the same point $x$,then for the expression $cx^2 + ax + b$:
- AMinimum value $= \frac{4b}{3}$
- BMaximum value $= \frac{4a}{3}$
- CMinimum value $= \frac{3a}{4}$
- DMaximum value $= \frac{3b}{4}$
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View SolutionMatch the following quadratic expressions with their minimum values:
Quadratic expression The minimum value i) $x^2 + 4x + 6$ a) $1$ ii) $x^2 - 2x + 5$ b) $2$ iii) $x^2 + 6x + 18$ c) $4$ iv) $x^2 - 4x + 5$ d) $9$
| Quadratic expression | The minimum value |
|---|---|
| i) $x^2 + 4x + 6$ | a) $1$ |
| ii) $x^2 - 2x + 5$ | b) $2$ |
| iii) $x^2 + 6x + 18$ | c) $4$ |
| iv) $x^2 - 4x + 5$ | d) $9$ |
DifficultAP EAMCET 2017
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