Answered

write the quadratic equation of the following roots. simplify your answer
1. -3,-5
2.-2,-7
3. 5,3
4.-6,6
5. -3,-7​

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UK2019viz

✏️QUADRATIC

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Direction: Write the quadratic equation of the following roots. Simplify your answer.

1. -3 and -5

  • [tex]x = \text - 3 \: \: \: \: \: \: \: \: x = \text - 5[/tex]

  • [tex]x + 3 = 0 \: \: \: \: \: \: \: \: x + 5 = 0[/tex]

  • [tex](x + 3)(x + 5) = 0[/tex]

  • [tex] {x}^{2} + 5x + 3x + 15 = 0[/tex]

  • [tex] {x}^{2} + 8x + 15 = 0[/tex]

- Therefore, the standard form of a quadratic equation is:

  • [tex] \large \boxed{ \: \sf \green{{x}^{2} + 8x + 15 = 0 \: }}[/tex]

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2. -2 and -7

  • [tex]x = \text - 2 \: \: \: \: \: \: \: \: x = \text - 7[/tex]

  • [tex]x + 2 = 0 \: \: \: \: \: \: \: \: x + 7 = 0[/tex]

  • [tex](x + 2)(x + 7) = 0[/tex]

  • [tex] {x}^{2} + 7x + 2x + 14 = 0[/tex]

  • [tex] {x}^{2} +9x + 14 = 0[/tex]

- Therefore, the standard form of a quadratic equation is:

  • [tex] \large \boxed{ \: \sf \green{{x}^{2} + 9x + 14 = 0 \: }}[/tex]

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3. 5 and 3

  • [tex]x = 5 \: \: \: \: \: \: \: \: x = 3[/tex]

  • [tex]x - 5 = 0 \: \: \: \: \: \: \: \: x - 3 = 0[/tex]

  • [tex](x - 5)( x - 3) = 0[/tex]

  • [tex] {x}^{2} - 3x - 5x + 15 = 0[/tex]

  • [tex] {x}^{2} - 8x + 15 = 0[/tex]

- Therefore, the standard form of a quadratic equation is:

  • [tex] \large \boxed{ \: \sf \green{{x}^{2} - 8x + 15= 0 \: }}[/tex]

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4. -6 and 6

  • [tex]x = \text - 6 \: \: \: \: \: \: \: \: x = 6[/tex]

  • [tex]x + 6 = 0 \: \: \: \: \: \: \: \: x - 6 = 0[/tex]

  • [tex](x + 6)(x - 6) = 0[/tex]

  • [tex] {x}^{2} - 6x + 6x - 36 = 0[/tex]

  • [tex] {x}^{2} - 36 = 0[/tex]

- Therefore, the standard form of a quadratic equation is:

  • [tex] \large \boxed{ \: \sf \green{{x}^{2} - 36= 0 \: }}[/tex]

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5. -3 and -7

  • [tex]x = \text - 3 \: \: \: \: \: \: \: \: x = \text - 7[/tex]

  • [tex]x + 3 = 0 \: \: \: \: \: \: \: \: x + 7 = 0[/tex]

  • [tex](x + 3)(x + 7) = 0[/tex]

  • [tex] {x}^{2} + 7x + 3x + 21 = 0[/tex]

  • [tex] {x}^{2} + 10x + 21 = 0[/tex]

- Therefore, the standard form of a quadratic equation is:

  • [tex] \large \boxed{ \: \sf \green{{x}^{2} + 10x + 21= 0 \: }}[/tex]

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