If one of the roots of | 3 &5 x 7 x 7 x 5 3 | = 0 is -10,then the other roots are

Question

If one of the roots of | 3 &5 x 7 x 7 x 5 3 | = 0 is -10,then the other roots are (A) 3, 7 (B) 4 , 7 (C) 3, 9 (D) 3,4

Tardigrade Admin · Accepted Answer

Given, | 3 &5 x 7 x 7 x 5 3 | = 0 ⇒ 3(3x - 35) - 5(21 - 7x) + x(35 - x2) = 0 ⇒ 9x - 105 - 105 + 35x + 35x - x3 = 0 ⇒ x3 - 79x + 210 = 0 ⇒ (x + 10) (x - 3) (x -7) = 0 ⇒ x = -10, 3, 7

Q. If one of the roots of $∣ ∣ 37 x 5 x 5 x 73 ∣ ∣ = 0$ is -10,then the other roots are

3, 7

4 , 7

3, 9

3,4

Given, $∣ ∣ 37 x 5 x 5 x 73 ∣ ∣ = 0$
$\Rightarrow 3 (3 x - 35) - 5 (21 - 7 x) + x (35 - x^{2}) = 0$
$\Rightarrow 9 x - 105 - 105 + 35 x + 35 x - x^{3} = 0$
$\Rightarrow x^{3} - 79 x + 210 = 0$
$\Rightarrow (x + 10) (x - 3) (x - 7) = 0$
$\Rightarrow x = - 10, 3, 7$

Q. If one of the roots of ∣∣​37x​5x5​x73​∣∣​=0 is -10,then the other roots are

3, 7

4 , 7

3, 9

3,4

Given, ∣∣​37x​5x5​x73​∣∣​=0 ⇒ 3(3x−35)−5(21−7x)+x(35−x2)=0 ⇒ 9x−105−105+35x+35x−x3=0 ⇒ x3−79x+210=0 ⇒ (x+10)(x−3)(x−7)=0 ⇒ x=−10,3,7

Q. If one of the roots of $∣ ∣ 37 x 5 x 5 x 73 ∣ ∣ = 0$ is -10,then the other roots are

Given, $∣ ∣ 37 x 5 x 5 x 73 ∣ ∣ = 0$
$\Rightarrow 3 (3 x - 35) - 5 (21 - 7 x) + x (35 - x^{2}) = 0$
$\Rightarrow 9 x - 105 - 105 + 35 x + 35 x - x^{3} = 0$
$\Rightarrow x^{3} - 79 x + 210 = 0$
$\Rightarrow (x + 10) (x - 3) (x - 7) = 0$
$\Rightarrow x = - 10, 3, 7$