Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Answer:
x=5/2, x=3
Step-by-step explanation:
Solve the equation with quadratic formula
Step-by-step explanation:
[tex] \tt{2 {x}^{2} + x - 15 = 0}[/tex]
USING THE QUADRATIC FORMULA :
Here ,
- a = 2 , b = 1 and c = - 15
Substitute the values into the quadratic equation :
⇾ [tex] \tt{x \: = \: \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} \: }{2a} }[/tex]
⇾ [tex] \tt{x = \frac{ - 1\: ± \: \sqrt{ {1}^{2} - 4 \times 2 \times ( - 15) } }{2 \times 2}} [/tex]
Simplify
⇾ [tex] \tt{x = \frac{ -1 \:± \sqrt{1 - 8 \times ( - 15)} }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1\:± \: \sqrt{1 + 120} }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1 \:± \: \sqrt{121} }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1\: ± \: \sqrt{ {11}^{2} } }{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 1 \:± \: 11 }{4}} [/tex]
Now , we can split this into two answers because of the plus minus ( ± ) symbol.
Taking positive ( + ) sign :
⇾ [tex] \tt{x = \frac{ - 1+ 11}{4}} [/tex]
⇾ [tex] \tt{x = \frac{10}{4}} [/tex]
⇾ [tex] \boxed{ \tt{x = \frac{5}{2} }}[/tex]
Again , taking negative ( - ) sign :
⇾ [tex] \tt{x = \frac{ - 1 - 11}{4}} [/tex]
⇾ [tex] \tt{x = \frac{ - 12}{4}} [/tex]
⇾[tex] \boxed{ \tt{x = - 3}}[/tex]
☥ [tex] \red{ \bold{ \boxed{ \boxed{ \tt{Our \: final \: answer : x = \frac{5}{2} \: or \: - 3}}}}}[/tex]
⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆
[tex] \underline{ \underline{ \sf{Explore \: more !!}}} : [/tex]
There are various methods of solving quadratic equations. They are as follows :
- Solving a quadratic equation by factorisation method : In this method , the second order of polynomial ax² + bx + c is factorised and expressed as the product of two linear factors. Then each linear factors is separately solved to get the required solutions of the equation by applying zero factor property. In zero factor property , if p • q = 0 then either p = 0 or q = 0 .In other words , if the product of two numbers is 0 , then one or both of the numbers must be zero.
- Solving a quadratic equation by completing the square : In this method , we transpose the constant term ( c ) to R.H.S , then L.H.S to expressed as perfect square expression.
- Solving a quadratic equation by using formula : In solving a quadratic equation of the form ax² + bx + c = 0 by completing the square , we obtain two roots of x , which are :[tex] \sf{ \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a}} [/tex] and [tex] \sf{ \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a}} [/tex]. These roots can be written as [tex] \sf{x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} }{2a}} [/tex] where a is the coefficient of x² , b is the coefficient of x and c is the constant term. We use this formula to find the required solutions of the given quadratic equation.
Hope I helped! ツ
Have a wonderful day / night ! ♡
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
