Solve for x using desmos or the quadratic formula 2x^2 - 5x - 12 = 0

x = 4 or x = (-3)/2

Step-by-step explanation:

Solve for x over the real numbers:

2 x^2 - 5 x - 12 = 0

x = (5 ± sqrt((-5)^2 - 4×2 (-12)))/(2×2) = (5 ± sqrt(25 + 96))/4 = (5 ± sqrt(121))/4:

x = (5 + sqrt(121))/4 or x = (5 - sqrt(121))/4

sqrt(121) = sqrt(11^2) = 11:

x = (5 + 11)/4 or x = (5 - 11)/4

(5 + 11)/4 = 16/4 = 4:

x = 4 or x = (5 - 11)/4

(5 - 11)/4 = -6/4 = -3/2:

 x = 4 or x = (-3)/2

1. If it is intersection then it SHOULD be included in both the sets right? Now we know that odd numbers from 1-100 but the second set are multiples of 5 from 50-150! So we mainly need to look for common numbers which are ODD and are a MULTIPLE OF 5 BETWEEN 50 - 100!! So A={51,53,57,59,6199} B={55,60,65,7095} [We stop till 100 because set A has no such element] So what is A ∩ B here? A ∩ B = {All odd numbers and multiples of 5 between 50 - 100}