What are the roots of this quadratic equation?-10x^2+12x-9=0

Mathematics

1 answer:

Ugo [173]2 years ago

7 0

Answer:

Step-by-step explanation:

-10x² + 12x - 9 = 0

Multiply the whole equation by (-1)

10x² - 12x + 9 = 0

a = 10 ; b = -12 ; c = 9

D = b² - 4ac = (-12)² - 4*10*9

= 144 - 360

= -216

√D = √-216 = $\sqrt{2*2 * 3 * 3 * 2 *3 * i^{2}}$

$= 2*3*i*\sqrt{3*2}\\\\= 6i \sqrt{6}$

Roots = $\frac{-b + \sqrt{D}}{2a} ; \frac{-b-\sqrt{D}}{2a}$

$= \dfrac{-[-12]+6i\sqrt{6}}{2*10} \ ; \ \dfrac{-[-12] - 6i\sqrt{6}}{2*10}\\\\= \dfrac{12+6i\sqrt{6}}{20} ; \ \dfrac{12-6i\sqrt{6}}{20}\\\\\\= \dfrac{2*(6+3i\sqrt{6}}{20} ; \ \dfrac{2*(6-3i\sqrt{6}}{20}\\\\=\dfrac{6+3i\sqrt{6}}{10} ; \dfrac{6-3i\sqrt{6}}{10}$

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