Question

find the relationship between zeroes and coefficient of the polynomial
5x²-6x-8​

Answer 1

$\huge{\underline{\underline{\mathfrak{\sf{Answer-}}}}}$

$\huge \implies \large \sf \: {5x}^{2} - 6x - 8 \\ \huge \implies \large \sf \: 5 {x}^{2} - 10x + 4x - 8 \\ \huge \implies \large \sf \: 5x(x - 2) + 4(x - 2) \\ \huge \implies \large \sf \: (5x + 4)(x - 2) \\ \huge \implies \ \sf \: x = - \frac{ 4}{5} and \: x = 2$

$\huge{\underline{\tt{Verifying\: the\: relationship}}}$

$\huge \implies \large \sf \: \alpha + \beta = \frac{ - b}{a} \\ \huge \implies \large \sf \: (\frac{ - 4}{5} ) + 2 = \frac{6}{5} \\ \huge \implies \large \sf \: \frac{ - 4 + 10}{5} \\ \huge \implies \large \sf \: \frac{6}{5} \\ \huge \implies \large \sf \: \alpha \times \beta = \frac{c}{a} \\ \huge \implies \large \sf \: \frac{ - 4}{5} \times 2 = \frac{ - 8}{5} \\ \huge \implies \large \sf \: \frac{ - 8}{5} \\ \\ \huge \implies \large \sf \: l.h.s = r.h.s \: in \: both \: cases \: \\ \\ \huge \implies \large \tt \: hence \: verified$