Question

-
$4 - 11x = 3x {}^{2}$
​

Answer 1

Solution:-

Method 1

=> We have equation

$\rm \implies3 {x}^{2} + 11x - 4 = 0$

Splitting into middle term

$\rm \implies3 {x}^{2} + 12x - x - 4$

$\rm \implies3x(x + 4) - 1(x + 4) = 0$

$\rm \implies(3x - 1)(x + 4) = 0$

$\rm \implies \: 3x = 1 \: \: and \: x = - 4$

$\rm \implies \: x = \dfrac{1}{3} \: and \: x = - 4$

Method 2 by quadratic formula

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

equation is

$\rm \implies3 {x}^{2} + 11x - 4 = 0$

So compare with

$\rm \implies \: a {x}^{2} + bx + c = 0$

So we get

$\rm \implies \: a = 3 \: , \: b = 11 \: \: and \: c = - 4$

Put the value on formula

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\rm \implies \: x = \dfrac{ - 11 \pm \sqrt{ {11}^{2} - 4 \times 3 \times - 4 } }{2 \times 3}$

$\rm \implies \: x = \dfrac{ - 11 \pm \sqrt{121 +48} }{6}$

$\rm \implies \: x = \dfrac{ - 11 + \sqrt{169} }{6} \: \: and \: x = \dfrac{ - 11 - \sqrt{169} }{6}$

$\rm \implies \: x = \dfrac{ - 11 + 13}{6} \: and \: x = \dfrac{ - 11 - 13}{6}$

$\rm \implies \: x = \dfrac{2}{6} \: \: and \: \: x = \dfrac{ - 24}{6}$

$\rm \implies \: x = \dfrac{1}{3} \: and \: x = - 4$

Answer 2

ANSWER:

=>3x^2+11x-4=0

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