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

Q1:

Given that πΏ + 3 and π + 3 are the roots of the equation π₯ + 8 π₯ + 1 2 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ and π .

Q2:

If πΏ and π are the roots of the equation π₯ β 1 9 π₯ + 9 = 0 ο¨ , find, in its simplest form, the quadratic equation whose roots are πΏ β 2 and π β 2 .

Q3:

Given that πΏ and π are the roots of the equation π₯ + π₯ β 2 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ + π 2 and π + πΏ 2 .

Q4:

Given that πΏ and π are the roots of the equation 3 π₯ + 1 6 π₯ β 1 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ 2 and π 2 .

Q5:

If πΏ and π are the roots of the equation 2 π₯ β 3 π₯ + 1 = 0 2 , find, in its simplest form, the quadratic equation whose roots are 2 πΏ 2 and 2 π 2 .

Q6:

Given that πΏ and π are the roots of the equation 3 π₯ + 6 π₯ + 2 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ π 2 and π πΏ 2 .

Q7:

Given that πΏ and π are the roots of the equation π₯ + 3 π₯ β 5 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ π 2 and π πΏ 2 .

Q8:

The roots of the equation π₯ + 6 π₯ + π = 0 2 are πΏ and π , where πΏ + π = 2 6 2 2 . Find the value of π , and determine, in its simplest form, the equation whose roots are πΏ π + π πΏ 2 2 and πΏ π .

Q9:

Given that πΏ and π are the roots of the equation π₯ β 3 π₯ + 1 2 = 0 2 , find, in its simplest form, the quadratic equation whose roots are 1 πΏ 2 and 1 π 2 .

Q10:

Given that πΏ and π are the roots of the equation π₯ β 1 3 π₯ β 5 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ + 1 and π + 1 .

Q11:

Given that 1 π and 1 πΏ are the roots of the equation π₯ β 8 π₯ β 1 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ π + 3 and πΏ + π + 6 .

Q12:

Given that πΏ and π are the roots of the equation π₯ β 9 π₯ β 7 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ β π and π β πΏ .

Q13:

If πΏ and π are the roots of the equation π₯ + 2 0 π₯ + 1 5 = 0 2 , what is the value of 1 π + 1 πΏ ?

Q14:

Without solving the equation 3 π₯ β 3 π₯ β 2 = π₯ + 5 π₯ β 7 , find the sum and the product of its roots.

Q15:

Given that πΏ and π are the roots of the equation π₯ β 2 π₯ + 5 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ 2 and π 2 .

Q16:

Given that πΏ and π are the roots of the equation 3 π₯ β 6 π₯ + 7 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ + π and πΏ π .

Q17:

The roots of the equation π π₯ + 6 π π₯ + π = 0 2 , where π β 0 , are πΏ and π . Given that πΏ β π = 2 οΌ 1 πΏ + 1 π ο , does π οΉ 9 π β π π ο = 3 6 π π 2 2 2 2 ?

Q18:

Without solving the equation ( 7 π₯ + 2 ) ( 8 π₯ + 1 ) = 0 , find the sum of its roots.

Q19:

What is the product of the roots of the equation π π₯ + 4 π π₯ + 8 π = 0 2 ?

Q20:

Given that β 3 π and β β 3 π are the two roots of the equation π₯ + π π₯ + π = 0 2 , find the values of π and π .

Q21:

Find the sum and the product of the roots of the equation ( 4 π₯ + 1 ) ( π₯ + 7 ) = ( π₯ + 4 ) ( π₯ β 8 ) without solving it.

Q22:

Given that πΏ and π are the roots of the equation π₯ β 1 6 π₯ β 6 = 0 2 , find, in its simplest form, the quadratic equation whose roots are πΏ + π and πΏ π .

Q23:

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

Q24:

Given that each root of the equation 5 π₯ + π = π₯ + 4 2 2 is the multiplicative inverse of the other, find all possible values of π .

Q25:

The sum of the roots of the equation π₯ β ( π + 6 ) π₯ β 6 π = 0 ο¨ ο¨ is equal to the product of the roots of the equation 3 π₯ + 9 π π₯ + π = 0 ο¨ ο¨ . Find the possible values of π .

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