Question

Find the zeros of the quadratic polynomial 2x sq -9-3x and verify the relationship between zeros and cofficients

Answer 1

${2x}^{2} - 3x - 9 = 0 \\ \\ = > 2 {x}^{2} - (6 - 3)x - 9 = 0 \\ \\ = > 2 {x}^{2} - 6x + 3x - 9 = 0 \\ \\ = > 2x(x - 3) + 3(x - 3) = 0 \\ \\ = > (x - 3)(2x + 3) = 0 \\ \\ \\ \\ x - 3 = 0 \\ \\ = > x = 3 \\ \\ \\ \\ \\ 2x + 3 = 0 \\ \\ = > x = \frac{ - 3}{2}$


verification

$sum \: of \: the \: zeroes \: = \frac{ - b}{a} \\ \\ = > 3 - \frac{3}{2} = \frac{3}{2} \\ \\ = > \frac{6 - 3}{2} = \frac{3}{2} \\ \\ = > \frac{3}{2} = \frac{3}{2} \\ \\ product \: of \: the \: zeroes \: = \frac{c}{a} \\ \\ = > 3 \times \frac{ - 3}{2} = \frac{ - 9}{2} \\ \\ = > \frac{ - 9}{2} = \frac{ - 9}{2}$



verified