The-number-of-roots-of-the-equation-2-x-2-7-x-6-0-

Question Number 49462 by Pk1167156@gmail.com last updated on 07/Dec/18

The number of roots of the equation

2 ∣ x ∣^{2} - 7 ∣ x ∣ + 6 = 0 .

Answered by tanmay.chaudhury50@gmail.com last updated on 07/Dec/18

∣ x ∣= x w h e n x > 0

= - x w h e n x < 0

n o w c o n s i d e r x > 0

2 x^{2} - 7 x + 6 = 0

2 x^{2} - 4 x - 3 x + 6 = 0

2 x (x - 2) - 3 (x - 2) = 0

(x - 2) (2 x - 3) = 0

x = 2 a n d \frac{3}{2}

w h e n x < 0

2 x^{2} + 7 x + 6 = 0

2 x^{2} + 4 x + 3 x + 6 = 0

2 x (x + 2) + 3 (x + 2) = 0

(x + 2) (2 x + 3) = 0

x = - 2 a n d \frac{- 3}{2}

s o x = \pm 2 a n d \pm \frac{3}{2}

Answered by mr W last updated on 07/Dec/18

l e t t =∣ x ∣⩾ 0

\Rightarrow 2 t^{2} - 7 t + 6 = 0

\Rightarrow (2 t - 3) (t - 2) = 0

\Rightarrow t = \frac{3}{2}, 2 (b o t h > 0 \Rightarrow o k)

\Rightarrow x = \pm \frac{3}{2}, \pm 2

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