Question

4x^2-4x+12=0
by using -b+root b^2-4ac/2a

Answer 1

Given Quadratic equation → 4x² - 4x + 12 = 0

Find out the value of x by using the quadratic formula.

$\boxed{ \bf{x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}$

where:

• a = 4
• b = -4
• c = 12

Substitute these values of a, b and c.

$\sf{x = \dfrac{ - ( - 4) \pm \sqrt{ {( - 4)}^{2} - 4(4)(12) } }{2(4)} }$

$\implies \tt{x = \dfrac{4 \pm \sqrt{16 - 192} }{8} }$

$\implies \tt{x = \dfrac{4 \pm \sqrt{ - 176} }{8} }$

$\implies \tt{x = \dfrac{4 \pm \sqrt{176}i }{8} }$

$\implies \tt{x = \dfrac{4 \pm \sqrt{16 \times 11} \: i }{8} }$

$\implies \tt{x = \dfrac{4 \: \pm \: 4\sqrt{11} \: i }{8} }$

$\implies \tt{x = \dfrac{4(1 \pm \sqrt{11}i) }{4} }$

$\therefore \boxed{ \bf{x = 1 + \sqrt{11}\: i \: \: or \: \: x = 1 - \sqrt{11}\: i }}$

Answer 2

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