Consider the graph of $f (x) = a x^{2} + b x + c$ in the given figure such that $l (A B) = 1, l (A C) = 4$ and $b^{2} - 4 a c = 4$ , then value of $(a + b + c)$ is equal to

1

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9

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10

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26

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Solution

The correct option is C $26$
$- \frac{D}{4 a} = 1 \Rightarrow D = - 4 a$

$∵ D = b^{2} - 4 a c = 4 \Rightarrow a = 1$

Also $\frac{- b}{2 a} = - 4 \Rightarrow b = 8$

$b^{2} - 4 a c = 4 \Rightarrow 644 c = 4$ or $c = 17$

$∴ a + b + c = 26$

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Similar questions

Q. The graph of

f (x) = a x^{2} + b x + c

is shown below, such that

b^{2} - 4 a c = - 4.

If the length of segment

A B

and

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are

1

and

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respectively, then the value of

(a + b + c)

is equal to

Q. The graphs of the two equations

y = a x^{2} + b x + c

and

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a

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b^{2} - 4 a c

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Let $f (x) = a x^{2} + b x + c$ . Then, match the following.
$\begin{matrix} a. Sum of roots of f(x) = 0 & 1. - \frac{b}{a} b. Product of roots of f(x) = 0 & 2. \frac{c}{a} c. Roots of f(x) = 0 are real and distinct & 3. b^{2} - 4 a c = 0 d. Roots of f(x) = 0 are real and identical. & 4. b^{2} - 4 a c > 0 \end{matrix}$