First slide

Theory of equations

Question

$If a < 0 and a - b + c = a - 3 b + 9 c = 0, then the quadratic expression y = a x^{2} + b x + c$
$will attains its maximum value of x = k, the k is:$

Moderate

A

$- \frac{1}{3}$
B

$- \frac{2}{3}$
C

1
D

$- \frac{4}{3}$

Solution

$Given that f (x) = a x^{2} + b x + c$
$Also a - b + c = 0 \Rightarrow f (- 1) = 0$
$And a - 3 b + 9 c = 0 \Rightarrow f (- \frac{1}{3}) = 0$
$∴ Roots of the equation are - 1 and - \frac{1}{3}$
$∴ k = \frac{(- 1) + (- \frac{1}{3})}{2}$
$\Rightarrow k = - \frac{2}{3}$
$Maximum value of y = c x^{2} + b x + c will appear at x = - \frac{2}{3} = k$

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