Question

Find the zeros of p(x) = x²-3x-28 and verify the relation between zeros

Answer 1

$\huge\underline\red{Answer}$

$\huge \implies \large \sf \: {x}^{2} - 3x - 28 \\ \\ \huge \implies \large \sf \: {x}^{2} - 7x + 4x - 28 \\ \\ \huge \implies \large \sf \: x(x - 7) + 4(x - 7) \\ \\ \huge \implies \large \sf \: (x - 7)(x + 4) \\ \\\huge \implies \large \sf \: zeros \:are \:7 \:and\:-4$

$\Large{\underline{\rm{\blue{verifying\: the\: relationship}}}}$

$\huge \implies \large \sf \: \alpha + \beta = \frac{ - b}{a} \\ \huge\implies\large\sf 7 + ( - 4) = - \frac{3}{1} \\ \huge \implies \large \sf \: 3 = 3 \\ \\ \huge \implies \large \sf \: \alpha \times \beta = \frac{c}{a} \\ \huge \implies \large \sf \: 7 \times ( - 4) = \frac{ - 28}{1} \\ \huge\implies\large\sf - 28 = - 28$

$\huge \therefore \large \sf \: LHS= RHS \\ \\ \huge \bullet \large \sf \: hence \: verified$