Question

find the zeros of the polynomial xsquare-3x -28 and verify the relationship between the zeroes and the coefficients of the polynomial

Answer 1

${x}^{2} - 3x - 28 = 0$
${x}^{2} - (7 - 4)x - 28 = 0$
${x }^{2} - 7x + 4x - 28 = 0$
$x(x - 7) + 4(x - 7) = 0$
$(x - 7)(x + 4) = 0$
$x = 7 \: \: and \: \: \: x = - 4$
$as \: we \: know \: that \: \alpha + \beta = - b \div a$
$\alpha + \beta = 7 - 4 = 3$
$and \: - b \div a = - ( - 3) \div 1 = 3$
$\alpha \beta = c \div a = - 28$
$and \: \alpha \beta = 7 \times ( - 4) = - 28$