Question

find the roots of the equation if they exist by applying​

Answer 1

Answer:

Refer to attachment.

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Step-by-step explanation:

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Answer 2

Question :

Find the roots of the equation, if they exist, by applying quadratic formula :

• 6x² + 5x - 6 = 0

Solution :

6x² + 5x - 6 = 0

Now, by quadratic formula :

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

In equation 6x² + 5x - 6 = 0:

• a = 6
• b = 5
• c = - 6

By filling values :

$\sf : \implies Roots = \dfrac{-(5) \pm \sqrt{(5)^{2} - 4(6)(-6)}}{2(6)}$

$\sf : \implies Roots = \dfrac{-5 \pm \sqrt{25 + 144}}{12}$

$\sf : \implies Roots = \dfrac{-5 \pm \sqrt{169}}{12}$

$\sf : \implies Roots = \dfrac{-5 \pm \sqrt{(13)^{2}}}{12}$

$\sf : \implies Roots = \dfrac{-5 \pm 13}{12}$

Hence, roots are :

• $\sf \dfrac{-5 + 13}{12} = \dfrac{8}{12} \dfrac{2}{3}$

• $\sf \dfrac{-5 - 13}{12} = \dfrac{-18}{12} \dfrac{- 3}{2}$

Therefore roots are :

• $\sf \dfrac{2}{3} \: and \: \dfrac{- 3}{2}$