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Figure 2.23 Show the Graph of the Polynomial F(X) = Ax2 + Bx + C for Which - Mathematics

MCQ

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

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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)`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 10 | Page 61
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