Question

19. If the expression y=8x – x2 – 15 is negative, then x lies in the interval- (A) (3,5) (B) (5,50) (C)(3,00) (D) (-0,3) (5,00) ​

Answer 1

Answer:

As the equation is less than 0 , take less than inequality.

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Answer 2

SOLUTION

TO DETERMINE

If the expression y = 8x - x² - 15 is negative, then x lies in the interval

EVALUATION

Here the given expression is

y = 8x - x² - 15

The expression is negative

$\displaystyle \sf{ \implies 8x - {x}^{2} - 15 < 0}$

$\displaystyle \sf{ \implies {x}^{2} - 8x + 15 > 0}$

$\displaystyle \sf{ \implies {x}^{2} - (3 + 5)x + 15 > 0}$

$\displaystyle \sf{ \implies {x}^{2} - 3x - 5x + 15 > 0}$

$\displaystyle \sf{ \implies (x - 3)(x - 5) > 0}$

$\displaystyle \sf{ \implies (x - 3) < 0 \: \: \: or \: \: \: (x - 5) > 0}$

$\displaystyle \sf{ \implies x < 3\: \: \: or \: \: \: x > 5}$

$\displaystyle \sf{ \implies x \in \: ( - \infty ,3) \: \cup \: (5 , \infty )}$

FINAL ANSWER

Hence the required interval is

$\displaystyle \sf{ \: ( - \infty ,3) \: \cup \: (5 , \infty )}$

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