Question

(a square -2 a ) square -23(a square -2a)+120​

Answer 1

Answer:

${a}^{4} - 19 {a}^{2} - 4 {a}^{3 } + 46a + 120$

Answer 2

((a^2) - 2a)^2 - 23((a^2) - 2a) + 120 = 0

Let (a^2) - 2a = x ——> 1

x^2 - 23x + 120 = 0

Splitting the middle term,

x^2 - 8x - 15x + 120 = 0

x(x - 8) - 15(x - 8) = 0

(x - 8)(x - 15) = 0

x - 8 = 0, x - 15 = 0

x = 8, 15

Substituting x = 8 in equation 1 we get,

(a^2) - 2a = 8

(a^2) - 2a - 8 = 0

(a^2) - 4a + 2a - 8 = 0

a(a - 4) + 2(a - 4) = 0

(a + 2)(a - 4) = 0

a = -2, 4

Substituting x = 15 in equation 1 we get,

(a^2) - 2a = 15

(a^2) - 2a - 15 = 0

(a^2) - 5a + 3a - 15 = 0

a(a - 5) + 3(a - 5) = 0

(a + 3)(a - 5) = 0

a = -3, 5

There roots of the qiven biquadratic equation are, a = -2, -3, 4 & 5 ——> Answer