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(1) in Each Question, put a (√) if the Expression is a Quadratic Equation and a (X) if It is Not.

(a)

(b)

(c)

(2) in Each Question, put a (√) if the Expression is a Quadratic Equation and a (X) if It is Not.

(a)

(b)

(c)

(3) in Each Question, put a (√) if the Expression is a Quadratic Equation and a (X) if It is Not.

(a)

(b)

(c)

A polynomial whose degree is 2 after simplification of polynomial is named as a Quadratic polynomial.

For example;

Here for given polynomial variable “a” highest degree is 2, hence given expression is quadratic polynomial.

Here for given polynomial variable “x” highest degree is 1, hence given expression is not a quadratic polynomial, it՚s a linear polynomial equation.

Here for given polynomial variable “x and y” highest degree is 3, hence given expression is not quadratic polynomial, it՚s a cubic polynomial equation.

Here for given polynomial variable “a” have highest degree is 3, hence given expression is not quadratic polynomial, it՚s a cubic polynomial equation.

Here for given polynomial variable “y” have highest degree is 2, hence given expression is quadratic polynomial.

Here for given polynomial variable “z” have highest degree is 3, hence given expression is not quadratic polynomial, it՚s a cubic polynomial equation.

Here for given polynomial variable “p” have highest degree is 2, hence given expression is quadratic polynomial.

Here for given polynomial variable “x” has highest degree is 2, hence given expression is quadratic polynomial.

Here for given polynomial variable “m” have highest degree is 3, hence given expression is not quadratic polynomial, it՚s a cubic polynomial equation.

(4) Simplify Each Question. Put a (√) if the Equation Can Be Written as a Quadratic Equation and a (X) if It Cannot.

(a)

(b)

(c)

First, we simplify the given equation,

Hence it is clear form derived equation that, equation have variable “x” has highest degree is 1.

Hence it՚s not a quadratic polynomial equation, it՚s a linear polynomial equation.

First, we simplify the given equation,

It is clear form derived equation that, equation have variable “x” has highest degree is 2.

So, it՚s a quadratic polynomial equation.

(5) Simplify Each Question. Put a (√) if the Equation Can Be Written as a Quadratic Equation and a (X) if It Cannot.

(a)

(b)

First, we simplify the given equation,

Hence it is clear form derived equation that, equation have variable “x” has highest degree is .

Hence it՚s not a quadratic polynomial equation.

First, we simplify the given equation,

Hence it is clear form derived equation that, equation have variable “x” has highest degree is 2.

So, it՚s a quadratic polynomial equation.

(6) Factorize the Given Quadratic Polynomials.

(a)

Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of

Hence,

Multiplication of coefficient

Now,

So,

Hence,

(7) Factorize the Given Quadratic Polynomials.

(a)

Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of

Hence

Multiplication of coefficient

Now,

So,

Hence,

(8) Factorize the Given Quadratic Polynomials.

(a)

Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of

Hence

Multiplication of coefficient

Now,

So,

Hence,

(a) if , then

(b) If , then

if , then

here given equation is

means any of two multiplied polynomials is equal to zero than and only than it is possible that multiplication of this polynomial is zero

so, we can say that,

If , then

Here given that means any of three variable one variable value is “0” than and only than it is possible that multiplication of all these three variables is zero.

Plus also given that out of this three variable , two variable multiplication is not zero, means none of this two variable having value is zero.

Hence remaining one variable should be zero,

So,

(a) if

(b)

if

here given equation is

is possible only if

So,

here given equation is

means any of these three multiplied polynomials is equal to zero than and only than it is possible that multiplication of this polynomial is zero

so, we can say that,

(11) in Each Question, Find the Roots of the Quadratic Equation.

(a)

Guess so,

Now, Compare this equation with identities

So, we have

Now,

so,

Now put the value of in above equation,

So, we have,

So,

(12) in Each Question, Find the Roots of the Quadratic Equation.

(a)

Guess so,

Now, Compare this equation with identities

So, we have

Now,

so,

Now put the value of in above equation,

So, we have,

So,

(13) Put a Tick (√) if the Given Values of P Are the Solutions of the Given Equation. Put a Cross (X) if They Aren՚t.

(a)

Here gives equation is

If are roots of given equation than, if we put this value (root) in place of variable than answer should be zero.

For root put the value of in given equation,

Hence is root of given equation,

For root put the value of in given equation,

Hence is root of given equation,

So, both given value of are roots of given equation.

So,

(14) Solve the Equation.

(a)

Now to factorize given equation; we made by summation of two such part that are factor of multiplication of coefficient of

Hence

Multiplication of coefficient

Now,

Hence

(15) in Each Question, the Roots of the Quadratic Equation Are Given. Find the Value of “P.”

(a)