Question

If alpha and 1/alpha are zero of 4x²-17x+k-4 find the value of alpha.

Answer 1

Product of zeroes =c/a
$\alpha \times 1 \div \alpha = c \div a$
1=(k-4)/4
4=k-4
K=8
Now eqn is
4x^2-17x+4=0
4x^2-16x-x+4=0
4x(x-4)-1(x-4)=0
(x-4)(4x-1)=0
Hence alpha=4or 1/4