Question

Attachment below:

Answer 1

brb

Answer 2

i'll help after you brbed :p

Answer 3

i am brbed..

Answer 4

@lgbasallote

Answer 5

\(x^2-3x-10=(x-5)(x+2) \)

a necessary and sufficient condition for \(x^2-3x-10=(x-5)(x+2)<0 \) is that \(-2<x<5\)

Answer 6

Yeah i have done that. But i am stuck in the portion after it, where it asks for the values of C and D

Answer 7

But it says a>=4.. i.e.option (6)

Answer 8

While finding C, we are concerned with necessary condition
and for D we need "sufficient" condition.

Answer 9

sorry it says necessary so \(a\) must be greater than or equal to 4 so \(|x−2|<a\) can cover all the interval \(−2<x<5\)

Answer 10

i mean its necessary to cover \( -2<x<5\) with \(|x-2|<a\) for having \(x^2-3x-10<0\)

Answer 11

what is the difference between necessary and sufficient condition? i am not getting it. and when a>4 say a=6, we have x>8 which seems contradictory.. i don't get it.