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Question
Figure 2.23 show the graph of the polynomial f(x) = ax2 + bx + c for which
Options
a < 0, b > 0 and c > 0
a < 0, b < 0 and c > 0
a < 0, b < 0 and c < 0
a > 0, b > 0 and c < 0
Solution
Clearly, f(x) = ax2 + bx + c represent a parabola opening downwards. Therefore, `a < 0`
` y= ax^2 + bx + c ` cuts y-axis at P which lies on `OY`. Putting x = 0 in ` y = ax^2 + bx + c `, we get y =c. So the coordinates P are `(0,c)`. Clearly, P lies on `(OY)`. Therefore `c > 0`
The vertex `(-b)/(2a), (-D)/(4a)` of the parabola is in the second quadrant. Therefore `-b /(2a)`, `b < 0`
Therefore `a < 0,b>0` and `c > 0`
Hence, the correct choice is `(b)`
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