*Notes: Factorization of Trinomials of the form . **To factorize this and . We will use this all across the solution.*

Solve by factorization:

Question 1:

Answer:

Question 2:

Answer:

Question 3:

Answer:

Question 4:

Answer:

Question 5:

Answer:

Question 6:

Answer:

Question 7:

Answer:

Question 8:

Answer:

Question 9:

Answer:

Question 10:

Answer:

Question 11:

Answer:

Question 12:

Answer:

Question 13:

Answer:

Let

Hence when ,

and

when ,

Hence

Question 14:

Answer:

Let

Hence when ,

and

when ,

Hence

Question 15:

Answer:

Question 16:

Answer:

Question 17:

Answer:

Question 18:

Answer:

Question 19:

Answer:

Question 20:

Answer:

Question 21: Find the quadratic equation whose solution set is i) ii) iii) iv)

Answer:

i)

ii)

iii)

iv)

Question 22: Find the value of , if and .

Answer:

Substituting

Question 23: Find the value of , if and

Answer:

Substituting

Question 24: Use the substitution to solve for , if .

Answer:

Therefore

Hence, if

Hence, if

Question 25: Without solving for the quadratic equation , find whether is a solution of this equation or not.

Answer:

Substituting

LHS

RHS

Hence is a root of the equation.

Question 26: Determine whether is a root of the equation or not.

Answer:

Hence is a not root of the equation.

Question 27: If is a solution of the quadratic equation ; find the value of .

Answer:

Substituting

Question 28: If and are solutions of quadratic equation , find the value of .

Answer:

and

Substituting

… … … … i)

Similarly,

… … … … ii)

Solving i) and ii)

We get

Question 29: In quadratic equation has one root as ; find the value of m and the other root of the equation.

Answer:

Substituting

Sustituting

Hence the other root is

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