Question

Solve the question plzz​

Answer 1

Here is your solution :-

x^3 -3x^2 +3x+k

p (3) = 3^3 -3×3^2+ 3×3 +k

=27-27+9+k

9 +k

= 9+ k =0

k = -9

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :}}}}$

k = - 9

$\mathfrak{\large{\underline{\underline{Explanation :}}}}$

f(x) = x³ - 3x² + 3x + k

Given :3 is a zero of f(x)

So, f(3) = 0

By substituting x = 3 in f(x) :

(3)³ - 3(3)² + 3(3) + k = 0

27 - 3(9) +9 + k = 0

27 - 27 + 9 + k = 0

0 + 9 + k = 0

9 + k = 0

$\boxed{k = - 9}$

Definitions :

Zero of a polynomial : We say that a zero of a polynomial p(x) is the value of x, which p(x) is equal to zero. this value is also called a root of the polynomial p(x).

Polynomial : An algebraic expression in which the variables involved have only non-zero negative integral powers is called a polynomial.

Cubic polynomial : A polynomial of degree 3 is called the cubic polynomial.

• If the variable in a polynomial is x, we made not the polynomial by p(x), q(x) or r(z) etc.

e.g. p(x) = 3x² + 2x + 1

q(x) = x³ - 5x² + x - 7

r(y) = y³ - 1

t(z) = z² + 5z + 3