Question

If α, β are the zeros of the polynomial x² − 5x + c and α − β = 1, then c = ?

(a) 0
(b) 1
(c) 4
(d) 6

Answer 1

$$\begin{gathered} \left(\text{d}\right)6 \\ \mathrm{Given}:\mathrm{\alpha }\text{and}\mathrm{\beta }\text{are the zeroes of}{x}^2-5x+c. \\ \mathrm{Also},\mathrm{\alpha }\text{-}\mathrm{\beta }\text{=1} \\ \therefore \mathrm{\alpha }+\mathrm{\beta }=5 \\ \text{Solving}\mathrm{\alpha }\text{+}\mathrm{\beta }\text{= 5 and}\mathrm{\alpha }\text{-}\mathrm{\beta }\text{=1, we get}\mathrm{\alpha }\text{=3 and}\mathrm{\beta }\text{=2.} \\ \mathrm{Since}\text{3 is a zero of the polynomial}{x}^2-5x+c,\mathrm{we}\mathrm{have}: \\ {3}^2-5\times 3+c=0 \\ =>c=6 \end{gathered}$$