7x^2 19x 6 = 0 ⇒ 7x^2 21x + 2x 6 = 0 ⇒ 7x(x 3) + 2(x 3) = 0 ⇒ (7x+2)(x 3) = 0 Now, this means either (7x+2)=0 or (x 3) = 0. ...

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Solving a Quadratic Equation by Factorization Method

Solve 7x2 -...

Question

Solve
$7 x^{2} - 19 x - 6 = ?$

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Solution

$7 x^{2} - 19 x - 6 = 0$
$\Rightarrow 7 x^{2} - 21 x + 2 x - 6 = 0$
$\Rightarrow 7 x (x - 3) + 2 (x - 3) = 0$
$\Rightarrow (7 x + 2) (x - 3) = 0$
$N o w, t h i s m e a n s e i t h e r (7 x + 2) = 0 o r (x - 3) = 0.$
$7 x + 2 = 0 \Rightarrow x = \frac{- 2}{7}$
$x - 3 = 0 \Rightarrow x = 3$
$H e n c e t h e t w o r o o t s o f t h i s q u a d r a t i c e q u a t i o n a r e \frac{- 2}{7} a n d 3.$

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