Answer:
Answer:
[tex]{ \rm{ \hookrightarrow{ \blue{ {x}^{2} + 6x + 9 }}}} \\ { \rm{ \hookrightarrow{ \red{ {x}^{2} - 9 }}}}[/tex]
Step-by-step explanation:
» General Quadratic expression:
[tex] { \rm{y = {x}^{2} - (sum \: of \: roots)x + (product \: of \: roots)}}[/tex]
» For (-3, -3), roots are -3 and -3
• Sum of roots:
[tex]{ \tt{sum = - 3 + - 3}} \\ { \tt{sum = - 6}}[/tex]
• Product of roots:
[tex]{ \tt{product = - 3 \times - 3}} \\ { \tt{product = 9}}[/tex]
• Equation:
[tex]{ \underline{ \underline{ \tt{ \: y = {x}^{2} + 6x + 9 \: }}}}[/tex]
» For (3, -3), roots are 3 and -3
• Sum of roots:
[tex]{ \tt{sum = - 3 + 3}} \\ { \tt{sum = 0}}[/tex]
• Product of roots:
[tex]{ \tt{product = - 3 \times 3}} \\ { \tt{product = - 9}}[/tex]
• Equation:
[tex]{ \underline{ \underline{ \tt{ \: y = {x}^{2} - 9 \: }}}}[/tex]
The system of two quadratic equation is
x² + 6x + 9 = 0
x² - 9 = 0
"A quadratic equation is an algebraic equation of the second degree in 'x'. The quadratic equation in its standard form is ax² + bx + c = 0, where 'a'(a ≠ 0) and 'b' are the coefficients, 'x' is the variable, and 'c' is the constant term."
The solution of the first equation in the system is (- 3, - 3).
Therefore, the equation will be
[x - (- 3)] [x - (- 3)] = 0
⇒ (x + 3)(x + 3) = 0
⇒ (x + 3)² = 0
⇒ x² + 6x + 9 = 0
The solution of the second equation in the system is (3, - 3).
Therefore, the equation will be
[x - 3] [x - (- 3)] = 0
⇒ (x - 3)(x + 3) = 0
⇒ (x)² - (3)² = 0
⇒ x² - 9 = 0
Learn more about quadratic equation here: https://brainly.com/question/16993652
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