Question

The number to be added to the polynomial x²–5x+4,so that 3 is the zero of the polynomial is ​

Answer 1

$p(x) = {x}^{2} - 5x + 4 \\ \\ let \: \: k \: be \: \: the \: number \: \: added \: so \: that \: p(3) = 0 \\ \\ f(x) = {x }^{2} - 5x + 4 + k \\ x = 3 \\ \\ {3 }^{2} - 5(3) + 4 + k = 0 \\ \\ 9 - 15 + 4 + k = 0 \\ \\ k - 2 = 0 \\ \\ k = 2 \\ \\ therefore \: \: 2 \: must \: be \: added \: to \: p(x)$

hope it helps

Answer 2

→ p (x) = x² −5x + 4

Let k be the number added so that p(3)=0.

→ f(x)=x²−5x+4+k

→ x=3

→ 3²−5(3)+4+k=0

→ 9−15+4+k=0

→ k−2=0

→ k=2

Therefore 2 must be added to p(x).