Question

if (-5) is a zero of a polynomial p(x)=xto the power 2 +11x+k. then calculate the value of k​

Answer 1

ATQ, -5 is a zero of polynomial p(x) = x² + 11x + k

so the remainder must come zero when p(x) is divided by -5

putting value -5 in p(x)

➡ p(-5) = (-5)² + 11(-5) + k = 0

➡ p(-5) = 25 - 55 + k = 0

➡ p(-5) = -30 + k = 0

➡ k = 30

verification :-

LHS = (-5)² - 11(-5) + 30

= 25 - 55 + 30

= -30 + 30

= 0

RHS = 0 (since remainder is 0 when polynomial is divided by it's zero)

LHS = RHS

hence, the value of k is 30