# what should be added to the polynomial x ^2-5x+4 so that 3 is the zero of the polynomial

### Asked by hvsl123 | 24th Jun, 2021, 05:30: PM

Expert Answer:

### Let f(x) = x^{2 }-5x + 4
Let g(x) = f(x) +k = x^{2} -5x +(4+k)
if 3 is zero of polynomial g(x) , then g(3) = 0
g(3) = (3)^{2} -5(3) +(4+k) = (4+k) - 6 = 0 or k = 2
If we add 2 to polynomial ( x^{2 }-5x + 4 ) , Then polynomial becomes ( x^{2 }-5x + 6 )
3 is zero of polynomial ( x^{2 }-5x + 6 )

^{2 }-5x + 4

^{2}-5x +(4+k)

^{2}-5(3) +(4+k) = (4+k) - 6 = 0 or k = 2

^{2 }-5x + 4 ) , Then polynomial becomes ( x

^{2 }-5x + 6 )

^{2 }-5x + 6 )

### Answered by Thiyagarajan K | 19th Sep, 2021, 04:22: PM

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