Question

let p(x)=x²-4x+3. find the value of p(0),p(1),p(2),p(3)and obtain zeroes of the polynomial p(x)​

Answer 1

★Qᴜᴇsᴛɪᴏɴ :-

ʟet p(x)=x²-4x+3. find the value of p(0),p(1),p(2),p(3)and obtain zeroes of the polynomial p(x).

★Tᴏ ғɪɴᴅ :-

• the value of p(0),p(1),p(2),p(3)
• zeroes of the polynomial p(x)

★Mᴇᴛʜᴏᴅ :-

We will firstly substitute the value of 'x' as 0, 1 , 2, and 3.

to obtain the zeros of the polynomial we will find the factors of polynomial ( x² - 4x +3)

★Sᴏʟᴜᴛɪᴏɴ :-

︎︎︎Solving for p(0)

p(x) = x² - 4x +3

p(0) = 0² - 4(0) + 3

p(0) = 3

︎︎︎Solving for p(1)

p(x) = x² - 4x +3

p(1) = 1² - 4(1) +3

p(1) = 1 - 4 +3

p(1) = 0

︎︎︎Solving for p(2)

p(x) = x² - 4x +3

p(2) = 2² - 4(2) + 3

p(2) = 4 - 8 +3

p(2) = -1

︎︎︎Solving for p(3)

p(x) = x² - 4x +3

p(3) = 3² - 4(3) +3

p(3) = 9 - 12 +3

p(3) = 0

Now we have to find zeroes of p(x)

For x = 1 , 3 ....p(x) = 0

Hence, zeroes are 1 and 3

★Vᴇʀɪғɪᴄᴀᴛɪᴏɴ :-

x² - 4x + 3 = 0

x² -3x - x +3 =0

x( x - 3) - 1( x - 3) =0

( x - 1) ( x - 3) =0

x = 1 ........x = 3.............(verified)