Question

there are two factors of -36 such thatone factor is 11 less than half of the other factor. choose all the pairs of these factors. -2 and 18 , -6 and 6, 3 and -12 , 4 and 9

Answer 1

Let one factor be x. Second factor is 11 less than half of this factor, so second factor will be (0.5x - 11). The product of these two factors is -36.

So,

$-36=x(0.5x-11) \\ \\ -36=0.5 x^{2} -11x \\ \\ -72= x^{2} -22x \\ \\ x^{2} -22x+72=0 \\ \\ x^{2} -18x-4x+72=0 \\ \\ x(x-18)-4(x-18)=0 \\ \\ (x-4)(x-18)=0 \\ \\ x=4, x=18$

If,
x = 4, the other factor will be = 0.5(4) - 11 = - 9
If,
x = 18, the other factor will be = 0.5(18) - 11 = -2

So, there are two possible set of factors.
1) 4 and -9
2) -2 and 18

From these -2 and 18 is available in the options. So this is the correct answer.