find the number of solutions 2X2 = 11 X - 10

Answer 1

If the question simply wants to know how many (real) solutions there are, then you only need to the look at the discriminate of 2x² - 11x + 10 = 0. The discriminate is b²-4ac. If the discriminate is positive, there are two roots or solutions, if it is zero, there is one root or solution, and if it is negative, there are no real roots - but there are imaginary roots!

If you plug a = 2, b =-11, and c = 10 into b²-4ac, you get -11²-4(2)(10) which equals 41. Since the 41 is positive, there are two real roots or solutions.

Answer 2

2x² - 11x + 10 = 0

using the quadratic formula

x = -b ±√(b² - 4ac) / 2a

a = 2, b = -11, c = 10

x = 11 ± √(121 - 80) / 4

x = 11 ±√41 / 4

x = 4.35 or x = 1.149