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In this lesson, we will learn how to write a quadratic equation given its roots.

Q1:

Find, in its simplest form, the quadratic equation whose roots are 8 β 1 1 and β β 1 1 .

Q2:

Find the values of π for which one of the roots of the equation 6 π₯ β 7 2 π₯ + π = 0 2 is the square of the other.

Q3:

Given that β 1 and β 6 are the solutions of the equation π₯ + π π₯ + π = 0 2 , find the values of π and π .

Q4:

Given that π₯ = β 9 is a root of the equation π₯ + π π₯ = 3 6 2 , determine the value of π .

Q5:

If one of the roots of the equation 3 π₯ + 9 π₯ = 0 2 is a root of the equation π₯ + 1 2 π₯ + π = 0 2 , what is the value of π ?

Q6:

Given that 1 and 12 are the roots of the equation π₯ + π π₯ + π = 0 2 , find the values of π and π .

Q7:

Given that π₯ = 5 + 6 π is one of the roots of the equation β 4 π₯ + π π₯ β 2 4 4 = 0 2 , find the other root and the value of π .

Q8:

The sum, π , of the first π consecutive integers ( 1 + 2 + 3 + 4 + β― + π ) can be found using Starting from 1, how many consecutive integers are required to make a sum of 1β953?

Q9:

Find the solution set of π₯ β 5 π₯ + 1 2 5 = 1 8 5 2 in β .

Q10:

Find the positive number whose square is 12 more than four times the number.

Q11:

If πΏ and π are the roots of the equation π₯ + 1 0 π₯ + 9 = 0 2 , what is the value of πΏ + π 2 2 ?

Q12:

Given that π₯ = 2 is a solution of the equation π₯ + π π₯ β 2 4 = 0 2 , find the value of π .

Q13:

Find, in its simplest form, the quadratic equation whose roots are β 4 2 β 2 π 5 β 3 π and β 4 + 4 6 π 4 β 5 π .

Q14:

Given that 3 is a solution of the equation 9 π₯ + 7 π₯ + π = 0 2 , find the value of π .

Q15:

Without solving the equation β 3 π₯ β 1 6 π₯ + 6 3 = 0 2 , find the sum of its roots.

Q16:

Given that πΏ and πΏ 2 are the roots of the equation 4 π₯ + π π₯ + 3 2 = 0 2 , find the value of π .

Q17:

Given that the sum of the roots of the equation 8 π₯ + π π₯ + 1 8 = 0 2 is equal to their product, find the value of π .

Q18:

What is the simplest form of the quadratic equation whose roots are 1 3 2 and 5 3 ?

Q19:

What is the simplest form of the quadratic equation whose roots are β 6 and 1 4 5 ?

Q20:

Given that β 1 is one of the roots of the equation π₯ + π π₯ + 2 = 0 2 , find the value of π and the value of the other root.

Q21:

What is the product of the roots of the quadratic equation π π₯ + π π₯ + π = 0 2 ?

Q22:

If the two roots of the equation β 5 π₯ + 1 0 π₯ + π = 0 2 are equal, determine the value of π , then find the two roots.

Q23:

Given that a root of the equation π₯ + 1 8 π₯ + π = 0 2 is π₯ = β 3 , what is the value of π ?

Q24:

Find, in its simplest form, the quadratic equation whose roots are π + 3 π and π β 3 π .

Q25:

Find, in its simplest form, the quadratic equation whose roots are π + 8 π and π β 8 π .

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