Question

log[ex (5x-3/4x+2)1/3]​

Answer 1

Step-by-step explanation:

2x3 + x2 – 5x + 2; 1/2 , 1, -2

p(x) = 2x3 + x2 – 5x + 2

Zeros for this polynomial are 1/2 , 1, -2

p(1/2) = 2(1/2)3 + (1/2)2 – 5(1/2) + 2

= (1/4) + (1/4) – (5/2) + 2

= 0

p(1) = 2(1)3 + (1)2 – 5(1) + 2 = 0

p(-2) = 2(-2)3 + (-2)2 – 5(-2) + 2

= -16 + 4 + 10 + 2

= 0

Therefore, ½ , 1, and −2 are the zeroes of the given polynomial. Comparing the given polynomial with ax3 + bx2 + cx + d, we obtain a = 2, b = 1, c = −5, d = 2

Let us take α = 1/2 ,β = 1, γ = -2

α + β + γ = 1/2 + 1 + (-2) = –1/2 = –b/a

αβ + βγ + γα = 1/2 x 1 + 1(-2) + 1/2 (-2) = -5/2 = c/a

αβγ = 1/2 x 1 x (-2) = –1/1 = – 2/2 = –d/a

Therefore, the relationship between the zeroes and the coefficients is verified.