Worksheet: Forming a Quadratic Equation Using Another Quadratic Equation

Download

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−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

Q3:

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

Q4:

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

Q5:

If 𝐿 and 𝑀 are the roots of the equation 𝑥+20𝑥+15=0, what is the value of 1𝑀+1𝐿?

  • A−34
  • B−35
  • C−43
  • D43
  • E35

Q6:

Given that 𝐿 and 𝑀 are the roots of the equation 3𝑥−6𝑥+7=0, find, in its simplest form, the quadratic equation whose roots are 𝐿+𝑀 and 𝐿𝑀.

  • A3𝑥−13𝑥+14=0
  • B3𝑥+6𝑥+7=0
  • C3𝑥+7𝑥−6=0
  • D3𝑥+13𝑥+14=0
  • E3𝑥−6𝑥+7=0

Q7:

If 𝐿 and 𝑀 are the roots of the equation 𝑥−19𝑥+9=0, find, in its simplest form, the quadratic equation whose roots are 𝐿−2 and 𝑀−2.

  • A𝑥−23𝑥−25=0
  • B𝑥−23𝑥+32=0
  • C𝑥−15𝑥−25=0
  • D𝑥−15𝑥+32=0
  • E𝑥+15𝑥−25=0

Q8:

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

  • A𝑥−𝑥−5=0
  • B𝑥+4𝑥−5=0
  • C𝑥−4𝑥−5=0
  • D𝑥−4𝑥+9=0
  • E𝑥+𝑥−5=0

Q9:

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

Q10:

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

Q11:

Given that 𝐿 and 𝑀 are the roots of the equation 3𝑥+6𝑥+2=0, find, in its simplest form, the quadratic equation whose roots are 𝐿𝑀 and 𝑀𝐿.

  • A3𝑥−18𝑥−2=0
  • B3𝑥+6𝑥+2=0
  • C3𝑥−18𝑥+2=0
  • D3𝑥+18𝑥+2=0
  • E𝑥−18𝑥+2=0

Q12:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥+3𝑥−5=0, find, in its simplest form, the quadratic equation whose roots are 𝐿𝑀 and 𝑀𝐿.

  • A𝑥+15𝑥+25=0
  • B𝑥−15𝑥−125=0
  • C𝑥+15𝑥−125=0
  • D𝑥+8𝑥+25=0
  • E𝑥−8𝑥−125=0

Q13:

The roots of the equation 𝑥+6𝑥+𝑐=0 are 𝐿 and 𝑀, where 𝐿+𝑀=26. Find the value of 𝑐, and determine, in its simplest form, the equation whose roots are 𝐿𝑀+𝑀𝐿 and 𝐿𝑀.

  • A𝑐=10, 𝑥−25𝑥+150=0
  • B𝑐=5, 𝑥+25𝑥−150=0
  • C𝑐=31, 𝑥−25𝑥+35=0
  • D𝑐=−10, 𝑥+35𝑥+150=0
  • E𝑐=−5, 𝑥−25𝑥+150=0

Q14:

Given that 1𝑀 and 1𝐿 are the roots of the equation 𝑥−8𝑥−1=0, find, in its simplest form, the quadratic equation whose roots are 𝐿𝑀+3 and 𝐿+𝑀+6.

  • A𝑥−4=0
  • B𝑥−4𝑥−4=0
  • C𝑥+9𝑥+36=0
  • D𝑥+4𝑥−4=0
  • E𝑥+4=0

Q15:

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

Q16:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−16𝑥−6=0, find, in its simplest form, the quadratic equation whose roots are 𝐿+𝑀 and 𝐿𝑀.

  • A𝑥−16𝑥−6=0
  • B𝑥+10𝑥+96=0
  • C𝑥−10𝑥−96=0
  • D𝑥+10𝑥−96=0
  • E𝑥+16𝑥−6=0

Q17:

If 𝐿 and 𝑀 are the roots of the equation 2𝑥+19𝑥−11=0, find, in its simplest form, the quadratic equation whose roots are 2−𝐿 and 2−𝑀.

  • A2𝑥−27𝑥+28=0
  • B2𝑥−13𝑥+17=0
  • C𝑥+23𝑥+31=0
  • D2𝑥−27𝑥+35=0
  • E𝑥+27𝑥−35=0

Q18:

Given that 𝐿 and 𝑀 are the roots of the equation 2𝑥−21𝑥+4=0, find, in its simplest form, the quadratic equation whose roots are 2𝐿 and 2𝑀.

  • A𝑥−21𝑥+8=0
  • B𝑥+21𝑥+8=0
  • C𝑥−42𝑥+16=0
  • D2𝑥−21𝑥+8=0
  • E2𝑥+21𝑥+8=0

Q19:

If 𝐿 and 𝑀 are the roots of the equation 𝑥+17𝑥+1=0, find, in its simplest form, the quadratic equation whose roots are 3𝐿 and 3𝑀.

  • A𝑥−34𝑥+9=0
  • B𝑥+102𝑥+9=0
  • C𝑥+51𝑥+9=0
  • D𝑥+51𝑥+3=0
  • E𝑥−51𝑥+9=0

Q20:

Given that 𝐿 and 𝑀 are the roots of the equation 2𝑥−10𝑥+1=0, find, in its simplest form, the quadratic equation whose roots are 𝐿3 and 𝑀3.

  • A18𝑥−5𝑥+1=0
  • B18𝑥−30𝑥+1=0
  • C𝑥+30𝑥+1=0
  • D18𝑥+30𝑥−1=0
  • E18𝑥+30𝑥+1=0

Q21:

The roots of the equation 𝑥−4𝑥+2=0 are 𝐿 and 𝑀, where 𝐿>𝑀. Find, in its simplest form, the quadratic equation whose roots are 5𝐿−2𝑀 and 2𝐿−5𝑀.

  • A𝑥+14√2𝑥+62=0
  • B𝑥−14√2𝑥+62=0
  • C𝑥+4√7𝑥+82=0
  • D𝑥+2√2𝑥+62=0
  • E𝑥−2√2𝑥+62=0

Q22:

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

Q23:

Given that 𝑙 and 𝑚 are the roots of the equation 3𝑥+4𝑥−9=0, find, in its simplest form, the quadratic equation whose roots are 𝑙 and 𝑚.

  • A−9𝑥−16𝑥+57=0
  • B9𝑥+70𝑥+81=0
  • C9𝑥+124𝑥+81=0
  • D9𝑥−124𝑥+81=0
  • E9𝑥−70𝑥+81=0

Q24:

Given that 𝐿 and 𝑀 are the roots of the equation 𝑥−6𝑥−7=0, find, in its simplest form, the quadratic equation whose roots are 𝐿 and 𝑀.

  • A𝑥−50𝑥+49=0
  • B𝑥+𝑥+49=0
  • C𝑥+49𝑥+50=0
  • D𝑥−𝑥+49=0
  • E𝑥+50𝑥+49=0

Q25:

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

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.