# Grade 8 Quadratic Equations Worksheet Questions and Answers (For CBSE, ICSE, IAS, NET, NRA 2022)

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

(a)

(b)

(c)

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

(a)

(b)

(c)

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

(a)

(b)

(c)

Answers and Explanations

Answer 1 (a)

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

For example;

Here for given polynomial variable โaโ highest degree is 2, hence given expression is quadratic polynomial.

Answer 1 (B)

Here for given polynomial variable โxโ highest degree is 1, hence given expression is not a quadratic polynomial, itีs a linear polynomial equation.

Answer 1 (C)

Here for given polynomial variable โx and yโ highest degree is 3, hence given expression is not quadratic polynomial, itีs a cubic polynomial equation.

Answer 2 (a)

Here for given polynomial variable โaโ have highest degree is 3, hence given expression is not quadratic polynomial, itีs a cubic polynomial equation.

Answer 2 (B)

Here for given polynomial variable โyโ have highest degree is 2, hence given expression is quadratic polynomial.

Answer 2 (C)

Here for given polynomial variable โzโ have highest degree is 3, hence given expression is not quadratic polynomial, itีs a cubic polynomial equation.

Answer 3 (a)

Here for given polynomial variable โpโ have highest degree is 2, hence given expression is quadratic polynomial.

Answer 3 (B)

Here for given polynomial variable โxโ has highest degree is 2, hence given expression is quadratic polynomial.

Answer 3 (C)

Here for given polynomial variable โmโ have highest degree is 3, hence given expression is not quadratic polynomial, itีs a cubic polynomial equation.

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

(a)

(b)

(c)

Answer 4 (a) :

First, we simplify the given equation,

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

Hence itีs not a quadratic polynomial equation, itีs a linear polynomial equation.

Answer 4 (b) :

First, we simplify the given equation,

It is clear form derived equation that, equation have variable โxโ has highest degree is 2.

So, itีs a quadratic polynomial equation.

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

(a)

(b)

Answer 5 (a) :

First, we simplify the given equation,

Hence it is clear form derived equation that, equation have variable โxโ has highest degree is .

Hence itีs not a quadratic polynomial equation.

Answer 5 (b) :

First, we simplify the given equation,

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

So, itีs a quadratic polynomial equation.

(6) Factorize the Given Quadratic Polynomials.

(a)

Answer 6 (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)

Answer 7 (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)

Answer 8 (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,

(9) Answer the Following Questions.

(a) if , then

(b) If , then

**Answer 9 (a)** :

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,

So, our answer is,

**Answer 9 (b)** :

If , then

Here given that means any of three variable one variable value is โ0โ 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,

(10) Answer the Following Questions.

(a) if

(b)

**Answer 10 (a)** :

if

here given equation is

is possible only if

So,

**Answer 10 (b)** :

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,

So, our answer is,

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

(a)

Answer 11 (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)

Answer 12 (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 (โ) if the Given Values of P Are the Solutions of the Given Equation. Put a Cross (X) if They Arenีt.

(a)

Answer 13 (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)

Answer 14 (a) :

Hence

Multiplication of coefficient

Now,

Hence

(15) in Each Question, the Roots of the Quadratic Equation Are Given. Find the Value of โP.โ

(a)

Answer 15 (a) :

Here gives equation is

If are roots of given equation than, if we put this value (root) in place of variable (x) than answer is equal to zero.

For root put the value of in given equation,

For root put the value of in given equation,

Hence the value of โpโ are