MCQ
Suppose a parabola $y=a x^2+b x+c$ has two $x$ intercepts, one positive and one negative, and its vertex is $(2,-2)$. Then, which of the following is true?
- A$a b > 0$
- ✓$b c > 0$
- C$c a > 0$
- D$a+b+c > 0$
✓
Answer
Correct option: B.
$b c > 0$
b
(b)
(b)
We have, $y=a x^2+b x+c$
Parabola has two roots one is positive and one is negative.
Clearly, $c$ is negative
$a > 0$
$-\frac{b}{a} =2$
$\therefore \quad-\frac{b}{a} > 0$
$\therefore \quad b < 0$
$\therefore > 0$
Hence, option $(b)$ is correct.
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