Question

Solve using formula : 9x2 + 6x - 8 = 0​

Answer 1

Answer:

The roots of the given quadratic equation are

$\displaystyle{{\boxed{\red{\sf\:x\:=\:-\:\dfrac{4}{3}}}}\sf\:\quad\:OR\:\quad\:{\boxed{\red{\sf\:x\:=\:\dfrac{2}{3}}}}}$

Step-by-step-explanation:

The given quadratic equation is 9x² + 6x - 8 = 0.

We have to find the roots of the quadratic equation using formula method.

Now,

9x² + 6x - 8 = 0

Comparing with ax² + bx + c = 0, we get,

• a = 9
• b = 6
• c = - 8

Now,

b² - 4ac = 6² - 4 * 9 * ( - 8 )

⇒ b² - 4ac = 36 - 4 * ( - 72 )

⇒ b² - 4ac = 36 - 2 * 2 * ( - 36 ) * 2

⇒ b² - 4ac = 36 - 8 * ( - 36 )

⇒ b² - 4ac = 36 - ( - 288 )

⇒ b² - 4ac = 36 + 288

⇒ b² - 4ac = 324

$\displaystyle{\therefore\:\boxed{\red{\sf\:b^2\:-\:4ac\:=\:324\:}}}$

Now, we know that,

$\displaystyle{\pink{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^2\:-\:4ac}}{2a}}\sf\:\quad\:-\:-\:-\:[\:Quadratic\:Formula\:]}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:6\:\pm\:\sqrt{324}}{2\:\times\:9}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:6\:\pm\:\sqrt{18\:\times\:18}}{18}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:6\:\pm\:18}{18}}$

$\displaystyle{\implies\sf\:x\:=\:-\:\cancel{6}\:\left(\:\dfrac{1\:\pm\:3}{\cancel{18}}\:\right)}$

$\displaystyle{\implies\sf\:x\:=\:-\:\left(\:\dfrac{1\:\pm\:3}{3}\:\right)}$

$\displaystyle{\implies\sf\:x\:=\:-\:\left(\:\dfrac{1\:+\:3}{3}\:\right)\:\quad\:OR\:\quad\:x\:=\:-\:\left(\:\dfrac{1\:-\:3}{3}\:\right)}$

$\displaystyle{\implies\sf\:x\:=\:-\:\dfrac{4}{3}\:\quad\:OR\:\quad\:x\:=\:-\:\left(\:-\:\dfrac{2}{3}\:\right)}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:-\:\dfrac{4}{3}}}}\sf\:\quad\:OR\:\quad\:\underline{\boxed{\red{\sf\:x\:=\:\dfrac{2}{3}}}}}$