Question

Find the sum and product of the roots of (x+4)(x+5)=6​

Answer 1

Answer :-

$(x + 4)(x + 5) = 6 \\ = > x(x + 5) + 4(x + 5) = 6 \\ = > {x}^{2} + 5x + 4x + 20 - 6 = 0 \\ = > {x}^{2} + 9x + 14 = 0 \\ = > {x}^{2} + 7x + 2x + 14 = 0 \\ = > x(x + 7) + 2(x + 7) = 0 \\ = > (x + 7)(x + 2) = 0 \\ = > x + 7 = 0 \: \: or \: \: x + 2 = 0 \:(zero \: \: product \: \: rule) \\ = > x = - 7 \: \: or \: \: x = - 2 \\ = > x = - 7 \: \: or \: \: - 2$

The roots of the given equation are -7 and -2.

Sum of the roots = -7 + (-2) = -7 - 2 = -9

Product of the roots = -7 × -2 = 14