Worksheet: Forming a Quadratic Equation from its Roots

In this worksheet, we will practice writing a quadratic equation given its roots.

Q1:

Find, in its simplest form, the quadratic equation whose roots are 8√11 and βˆ’βˆš11.

  • Aπ‘₯βˆ’7√11π‘₯βˆ’88=0
  • Bπ‘₯+7√11π‘₯βˆ’88=0
  • Cπ‘₯βˆ’7π‘₯βˆ’88=0
  • Dπ‘₯βˆ’7√11π‘₯+88=0
  • Eβˆ’88π‘₯βˆ’7√11π‘₯βˆ’88=0

Q2:

What is the sum of the roots of the equation π‘₯βˆ’24=0?

Q3:

What is the simplest form of the quadratic equation whose roots are 132 and 53?

  • A6π‘₯+29π‘₯βˆ’65=0
  • B6π‘₯+49π‘₯+65=0
  • C2π‘₯βˆ’3π‘₯βˆ’65=0
  • D6π‘₯βˆ’49π‘₯+65=0

Q4:

Find, in its simplest form, the quadratic equation whose roots are π‘š+3𝑛 and π‘šβˆ’3𝑛.

  • Aπ‘₯βˆ’2π‘šπ‘₯+π‘šβˆ’9𝑛=0
  • Bπ‘₯+2π‘₯+π‘šβˆ’9𝑛=0
  • Cπ‘₯βˆ’6𝑛π‘₯+π‘šβˆ’9𝑛=0
  • Dπ‘₯βˆ’2π‘₯+π‘š+9𝑛=0
  • Eπ‘₯βˆ’2π‘šπ‘₯+π‘šβˆ’3𝑛=0

Q5:

Given that βˆ’1 and βˆ’6 are the solutions of the equation π‘₯+𝑏π‘₯+𝑐=0, find the values of 𝑏 and 𝑐.

  • A𝑏=6, 𝑐=7
  • B𝑏=βˆ’7, 𝑐=βˆ’6
  • C𝑏=βˆ’7, 𝑐=6
  • D𝑏=7, 𝑐=6
  • E𝑏=βˆ’6, 𝑐=βˆ’7

Q6:

Given that π‘₯=βˆ’9 is a root of the equation π‘₯+π‘šπ‘₯=36, determine the value of π‘š.

Q7:

If one of the roots of the equation 3π‘₯+9π‘₯=0 is a root of the equation π‘₯+12π‘₯+π‘Ž=0, what is the value of π‘Ž?

  • Aβˆ’27 or 0
  • Bβˆ’27
  • C27 or 0
  • D0

Q8:

If 𝐿 and 𝑀 are the roots of the equation π‘₯+10π‘₯+9=0, what is the value of 𝐿+π‘€οŠ¨οŠ¨?

Q9:

Given that βˆ’1 is one of the roots of the equation π‘₯+π‘Žπ‘₯+2=0, find the value of π‘Ž and the value of the other root.

  • Aπ‘Ž=3, other root =2
  • Bπ‘Ž=3, other root =βˆ’2
  • Cπ‘Ž=βˆ’3, other root =2
  • Dπ‘Ž=βˆ’3, other root =βˆ’2

Q10:

Given that a root of the equation π‘₯+18π‘₯+π‘˜=0 is π‘₯=βˆ’3, what is the value of π‘˜?

Q11:

If 𝐿 and 𝑀 are the roots of the equation π‘₯+2π‘₯βˆ’6=0, what is the value of 𝐿+π‘€οŠ©οŠ©?

Q12:

Find the values of 𝑐 for which one of the roots of the equation 6π‘₯βˆ’72π‘₯+𝑐=0 is the square of the other.

  • A24, βˆ’18
  • Bβˆ’24, 18
  • Cβˆ’64, 27
  • Dβˆ’384, 162
  • E384, βˆ’162

Q13:

Given that 1 and 12 are the roots of the equation π‘₯+π‘šπ‘₯+𝑛=0, find the values of π‘š and 𝑛.

  • Aπ‘š=12, 𝑛=βˆ’13
  • Bπ‘š=12, 𝑛=13
  • Cπ‘š=βˆ’13, 𝑛=12
  • Dπ‘š=13, 𝑛=12
  • Eπ‘š=βˆ’11, 𝑛=13

Q14:

Given that π‘₯=2 is a solution of the equation π‘₯+𝑏π‘₯βˆ’24=0, find the value of 𝑏.

Q15:

Given that 3 is a solution of the equation 9π‘₯+7π‘₯+π‘˜=0, find the value of π‘˜.

Q16:

Without solving the equation βˆ’3π‘₯βˆ’16π‘₯+63=0, find the sum of its roots.

  • Aβˆ’323
  • Bβˆ’163βˆ’9𝑖
  • Cβˆ’163
  • Dβˆ’316
  • Eβˆ’21

Q17:

Given that 𝐿 and 𝐿 are the roots of the equation 4π‘₯+𝑏π‘₯+32=0, find the value of 𝑏.

Q18:

Given that the sum of the roots of the equation 8π‘₯+𝑏π‘₯+18=0 is equal to their product, find the value of 𝑏.

Q19:

What is the product of the roots of the quadratic equation π‘Žπ‘₯+𝑏π‘₯+𝑐=0?

  • Aβˆ’π‘π‘
  • Bβˆ’π‘π‘Ž
  • Cπ‘π‘Ž
  • Dπ‘Žπ‘

Q20:

If the sum of the roots of the equation βˆ’3π‘₯+π‘˜π‘₯+11=0 is 4, what is the value of π‘˜?

Q21:

Given that 𝑙 and 4βˆ’π‘™ are the roots of the equation π‘₯βˆ’π‘šπ‘₯βˆ’17=0, find the value of π‘š.

Q22:

The difference between the roots of the equation 9π‘₯βˆ’4π‘₯βˆ’2=π‘οŠ¨ is βˆ’49. What is the value of 𝑐?

Q23:

The roots of the equation π‘šπ‘₯βˆ’12𝑛π‘₯+𝑙=0, where π‘šβ‰ 0 are 𝐿 and 𝑀. Given that 𝐿>𝑀 and πΏβˆ’π‘€=20, does 𝐿=10+6π‘›π‘š?

  • Ano
  • Byes

Q24:

If the product of the roots of the equation 6π‘₯+2π‘₯+π‘˜=0 is βˆ’4, what is the value of π‘˜?

Q25:

The roots of the equation 6π‘₯βˆ’π‘šπ‘₯+24=0 are positive numbers which are in the ratio 4∢9. What is the value of π‘š?

  • A133
  • B72
  • C26
  • D263

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