Question

(k-1)x2+kx+1 if one of the zero is 3 find k and zero of the polynomial​

Answer 1

Zero

• A number which makes the polynomial 0.

To find k: The given zero is x=3.

Here, x=3

→ $\sf{(k-1)\times(-3)^2+(-3k)+1=0}$

→ $\sf{9(k-1)-3k+1=0}$

→ $\sf{12k-8=0}$

$\sf{\therefore{k=\frac{2}{3} }$

To find the zero: We know that $\sf{k=\frac{2}{3} }$.

Here, $\sf{k=\frac{2}{3} }$

→ $\sf{-\frac{1}{3} x^2+\frac{2}{3} x+1=0}$

→ $\sf{x^2-2x-3=0}$

• Factorization Method

→ $\sf{(x-3)(x+1)=0}$

∴The solutions are $\sf{x=3}$, $\sf{x=-1}$

Therefore another zero is -1.