Lesson Worksheet: Forming a Quadratic Equation Using Another Quadratic Equation Mathematics

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In this worksheet, we will practice writing a quadratic equation given the roots of another quadratic equation.

Q1:

Given that 𝐿+3 and 𝑀+3 are the roots of the equation 𝑥+8𝑥+12=0, find, in its simplest form, the quadratic equation whose roots are 𝐿 and 𝑀.

  • A𝑥+17𝑥+34=0
  • B𝑥+14𝑥+45=0
  • C𝑥−17𝑥+31=0
  • D𝑥−17𝑥+19=0
  • E𝑥+17𝑥+19=0

Q2:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−13𝑥−5=0, find, in its simplest form, the quadratic equation whose roots are 𝐿+1 and 𝑀+1.

  • A𝑥−15𝑥+9=0
  • B𝑥−11𝑥+9=0
  • C𝑥+15𝑥+9=0
  • D𝑥−15𝑥+8=0
  • E𝑥+11𝑥+8=0

Q3:

Given that 𝐿 and 𝑀 are the roots of the equation 3𝑥+16𝑥−1=0, find, in its simplest form, the quadratic equation whose roots are 𝐿2 and 𝑀2.

  • A12𝑥−32𝑥−1=0
  • B𝑥+32𝑥−1=0
  • C12𝑥+32𝑥+1=0
  • D𝑥−32𝑥−1=0
  • E12𝑥+32𝑥−1=0

Q4:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−9𝑥−7=0, find, in its simplest form, the quadratic equation whose roots are 𝐿−𝑀 and 𝑀−𝐿.

  • A𝑥−18𝑥−109=0
  • B𝑥−109=0
  • C𝑥+109=0
  • D𝑥+18𝑥−109=0
  • E𝑥−95=0

Q5:

Given that 𝑙 and 𝑚 are the roots of the equation −𝑥+7𝑥−9=0, find, in its simplest form, the quadratic equation whose roots are 1𝑙 and 1𝑚.

  • A9𝑥+7𝑥+1=0
  • B63𝑥+81𝑥+7=0
  • C7𝑥−9𝑥−1=0
  • D9𝑥−7𝑥+1=0
  • E63𝑥−81𝑥+7=0

Q6:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−2𝑥+5=0, find, in its simplest form, the quadratic equation whose roots are 𝐿 and 𝑀.

  • A𝑥+14𝑥+25=0
  • B𝑥+8𝑥+25=0
  • C𝑥−6𝑥+25=0
  • D𝑥+6𝑥+25=0
  • E𝑥−6𝑥+10=0

Q7:

If 𝐿 and 𝑀 are the roots of the equation 2𝑥−3𝑥+1=0, find, in its simplest form, the quadratic equation whose roots are 2𝐿 and 2𝑀.

  • A2𝑥−5𝑥+2=0
  • B𝑥−5𝑥+1=0
  • C2𝑥+5𝑥+2=0
  • D𝑥−5𝑥+2=0
  • E2𝑥−5𝑥+1=0

Q8:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−3𝑥+12=0, find, in its simplest form, the quadratic equation whose roots are 1𝐿 and 1𝑀.

  • A𝑥−15𝑥+1=0
  • B144𝑥−15𝑥+1=0
  • C144𝑥+15𝑥+1=0
  • D144𝑥+5𝑥+1=0
  • E144𝑥−15𝑥−1=0

Q9:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−2𝑥+20=0, find, in its simplest form, the quadratic equation whose roots are 2 and 𝐿+𝑀.

  • A𝑥−34𝑥−36=0
  • B𝑥+34𝑥−72=0
  • C𝑥−34𝑥−72=0
  • D𝑥−36𝑥−36=0
  • E𝑥−36𝑥−72=0

Q10:

Given that 𝐿+6 and 𝑀+6 are the roots of the equation 𝑥−6𝑥−4=0, find, in its simplest form, the quadratic equation whose roots are 𝐿𝑀 and 𝑀𝐿.

  • A𝑥+24𝑥+16=0
  • B𝑥+24𝑥−64=0
  • C𝑥−24𝑥−64=0
  • D𝑥−24𝑥+16=0
  • E𝑥−10𝑥+24=0

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