Question

Out of the following equations, which equation has 3 as a solution ?
$(a) \: {x}^{2} - x - 6 = 0$
$(b) \: {x}^{2} + x - 6 = 0$
$(c) \: {x}^{2} - x + 6 = 0$
$(d) \: {x}^{2} + x + 6 = 0$
​

Answer 1

Answer:

Equation:- ∣x∣

2

+∣x∣−6=0

Case 1:- x>0

x→x

x

2

+x−6=0

x

2

+3x−2x−6=0

x(x+3)−2(x+3)=0

(x+3)(x−2)=0

x=2,−3 (−3 will be neglected because of x>0)

Case 2:-

x<0

x→−x

(−x)

2

+(−x)−6=0

x

2

−x−6=0

x

2

−3x+2x−6=0

x(x−3)+2(x−3)=0

(x−3)(x−2)=0

x=3,2 (3 will be neglected because of x<0)

Sum of the Real roots

⇒2+(−2)=0.

solution

Answer 2

ꜰɪʟᴛʀᴀᴛɪᴏɴ ɪꜱ ᴀ ᴘʀᴏᴄᴇꜱꜱ ᴜꜱᴇᴅ ᴛᴏ ꜱᴇᴘᴀʀᴀᴛᴇ ꜱᴏʟɪᴅꜱ ꜰʀᴏᴍ ʟɪQᴜɪᴅꜱ ᴏʀ ɢᴀꜱᴇꜱ ᴜꜱɪɴɢ ᴀ ꜰɪʟᴛᴇʀ ᴍᴇᴅɪᴜᴍ ᴛʜᴀᴛ ᴀʟʟᴏᴡꜱ ᴛʜᴇ ꜰʟᴜɪᴅ ᴛᴏ ᴘᴀꜱꜱ ᴛʜʀᴏᴜɢʜ ʙᴜᴛ ɴᴏᴛ ᴛʜᴇ ꜱᴏʟɪᴅ. ᴛʜᴇ ᴛᴇʀᴍ "ꜰɪʟᴛʀᴀᴛɪᴏɴ" ᴀᴘᴘʟɪᴇꜱ ᴡʜᴇᴛʜᴇʀ ᴛʜᴇ ꜰɪʟᴛᴇʀ ɪꜱ ᴍᴇᴄʜᴀɴɪᴄᴀʟ, ʙɪᴏʟᴏɢɪᴄᴀʟ, ᴏʀ ᴘʜʏꜱɪᴄᴀʟ. ᴛʜᴇ ꜰʟᴜɪᴅ ᴛʜᴀᴛ ᴘᴀꜱꜱᴇꜱ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ꜰɪʟᴛᴇʀ ɪꜱ ᴄᴀʟʟᴇᴅ ᴛʜᴇ ꜰɪʟᴛʀᴀᴛᴇ.