Question

10. Using the graph of y=x2-3x- 10. What is the correct way to write the solution of
x2-3x-10 < 0? ?
A. {x52}u**25)
B. 2 <x 55)
c.-22x25}
D. {X22}u {x55)​

Answer 1

Given : y = x² - 3x - 10

To Find :  solution of x² - 3x - 10 <  0

Solution:

y = x² - 3x - 10

=> y = x² - 5x + 2x - 10

=> y = x(x - 5) + 2(x - 5)

=> y = (x - 5)(x + 2)

x² - 3x - 10 < 0

=>  (x - 5)(x + 2) < 0

x = 5 , -2   => y = 0

x > 5 => y =  (+)(+) = + >  0  

-2 < x < 5  => y = (-)(+) = -  < 0

x < - 2 => y =   (-)(-) = +  >0

Hence  x ∈ ( - 2 , 5 )

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