Question

2. Să se afle rădăcinile polinoamelor:

a) P(x)= X⁴-15X²+54
b) P(X)=2X⁴-13X²+15​

Answer 1

Răspuns:

Explicație pas cu pas:

$a) P(x) = x^4 - 15x^2 + 54\\x^2 = u\\P(u) = u^2 - 15u + 54 = (u-9)(u-6) = 0\\u -9 = 0 => u = 9\\u - 6 = 0 => u = 6\\x^2 = 9 => x_1 = 3, x_2 = -3\\x^2 = 6 => x_3 =\sqrt{6}, x_4 = - \sqrt{6} \\\\b) P(x) = 2x^4 - 13x^2 + 15 \\x^2 = u\\P(u) = 2u^2 - 13u + 15 = (2u - 3)(u-5) = 0\\2u - 3 = 0 => 2u = 3 => u = \frac{3}{2}\\ u - 5 = 0 => u = 5\\x^2 = \frac{3}{2} => x_1 = \sqrt{\frac{3}{2}} , x_2 = -\sqrt{\frac{3}{2}}\\x^2 = 5 => x_3 =\sqrt{5}, x_4 = -\sqrt{5}$