Question

solve x³-9x²+24x-20=0​

Answer 1

Answer:

x3 - 9x2 + 24x - 20 = (x-2)(x-2)(x-5)

f(x)= x3 - 9x2 + 24x - 20

By the rational root theorem, any rational zeroes of f(x) are expressible in the form p/q for integers p, q with p a divisor of the constant term 20 and q a divisor of the coefficient 1 of the leading term .

That means that the only possible rational zeroes are:

+1, +2, +4, +5, +10, +20

trying each in turn, we find:

f(2) = 8 - 9(4) + 24(2) - 20 = 8 - 36 + 48 - 20 = 0

so x = 2 is a zero and (x - 2) a factor:

x3 - 9x2 + 24x - 20 = (x - 2)(x2 - 7x + 10)

Note that 7 = 2 + 5 and 10 = 2.5

so we find:

x2 - 7x + 10 = (x - 2)(x - 5)

putting it all together:

x3 - 9x2 + 24x -20 = (x - 2) (x - 2) (x - 5)

Answer 2

Answer:

give answer

Explanation:

plz give this answer