(a) Find the zeroes of the polynomial $p(x)=15x^2-19x+6$.
OR
(b) If...

Question

(a) Find the zeroes of the polynomial $p(x)=15x^2-19x+6$.
OR
(b) If one zero of the polynomial $p(x)=(k-1)x^2-(4k+1)x+10$ is 5, find the value of k.

Accepted Answer

**(a)** $15x^2-19x+6 = 15x^2-10x-9x+6 = 5x(3x-2)-3(3x-2)=(3x-2)(5x-3)$. Zeroes: $x=\frac23,\ x=\frac35$.

**(b)** Since $x=5$ is a zero: $(k-1)(25)-(4k+1)(5)+10=0 \Rightarrow 25k-25-20k-5+10=0 \Rightarrow 5k-20=0 \Rightarrow k=4$.