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:
Answer:
Question 4:
Answer:
Answer:
Answer:
Answer:
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
Answer:
Answer:
Answer:
Answer:
Answer:
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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