The equation (x-1)(x-2)(x-3)=24 has the real root equal to ' a ' and the complex roots b and c. Then the value of (b c/a), is

Question

The equation (x-1)(x-2)(x-3)=24 has the real root equal to ' a ' and the complex roots b and c. Then the value of (b c/a), is (A) (1/5) (B) -(1/5) (C) (6/5) (D) -(6/5)

Tardigrade Admin · Accepted Answer

cubic is x3-6 x2+11 x-30=0 (x-5)(x2-x+6)=0 Hence a=5 ; b c=6 ⇒ (b c/a)=(6/5)

Q. The equation $(x - 1) (x - 2) (x - 3) = 24$ has the real root equal to ' $a$ ' and the complex roots $b$ and $c$ . Then the value of $\frac{b c}{a}$ , is

$\frac{1}{5}$

$- \frac{1}{5}$

$\frac{6}{5}$

$- \frac{6}{5}$

cubic is $x^{3} - 6 x^{2} + 11 x - 30 = 0$
$(x - 5) (x^{2} - x + 6) = 0$
Hence $a = 5; b c = 6 \Rightarrow \frac{b c}{a} = \frac{6}{5}$

Q. The equation (x−1)(x−2)(x−3)=24 has the real root equal to ' a ' and the complex roots b and c. Then the value of abc​, is

51​

−51​

56​

−56​