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QUESTION: 1

Write the general form of a quadratic polynomia

Solution:

If the coefficient of x^{2} is zero , then the equation is not a quadratic equation , its a linear equation. So its necessary condition for the quadratic equation.

QUESTION: 2

One of the roots of the quadratic equation 6x^{2} – x – 2 = 0 is:

Solution:

*Multiple options can be correct

QUESTION: 3

Which of the following statement is TRUE?

Solution:

A quadratic equation in variable x is of the form ax^{2}+ bx + c = 0, where a, b, c are real numbers a ≠ o, because if a=0 then the equation becomes a linear equation.

If we can factorise ax^{2} + bx + c, a ≠ 0 into product of two linear factors then roots can be found by equating each factor to zero because if two factors are in multiplication and equal to zero then either of the factor is zero.

A real number R is said to be a root of the quadratic equation ax^{2} + bx + c = 0 if a(R)^{2} + bR + c = 0. , root means that the value gives answer equal to zero.

So all are correct.

QUESTION: 4

If n is a non negative integer, then a^{n}x ^{n} +…+ a _{1} x + a_{0} is a

Solution:

QUESTION: 5

The two positive numbers differ by 5 and square of their sum is 169 are

Solution:

QUESTION: 6

If 4 is a root of the equation x^{2} + 3x + k = 0, then k is

Solution:

4 is the solution , this means that if we put x=4 we get 0. So putting x=4 in the equation x^{2}+3x+k=0 we get 4^{2}+3*4+k=0

16+12+k=0 ⇒ k=-28

QUESTION: 7

If 8 is a root of the equation x^{2} – 10x + k = 0, then the value of k is:

Solution:

Let, p(x) = x²-10x+k

since, 8 is the root of p(x)

∴ p(8) = 0

8²-10(8)+k = 0

64-80+k = 0

-16+k = 0

⇒ k = 16 .

QUESTION: 8

Which of following is not a quadratic equation:

Solution:

QUESTION: 9

The solution of 5z^{2} = 3z is

Solution:

We have 5z^{2}=3z

5z^{2}-3z=0

z(5z-3)=0

So either z=0

Or 5z-3 =0 = z=⅗. So there are two solutions

QUESTION: 10

Which of the following equations has 2 as a root?

Solution:

QUESTION: 11

Which of the following equations has the sum of its roots as 3?

Solution:

*Multiple options can be correct

QUESTION: 12

Which of the following is not a quadratic equation:

Solution:

Option (B) and (D) , both are the correct answers. We have x(x + 1) + 8 = (x + 2) (x – 2)

=x^{2 }+ x + 8 = x^{2} - 4

= x = -12, which is not a quadratic equation

Also, in (B) (x + 2)^{2} = x^{3} – 4

=x^{2 }+4x + 4=x^{3 }- 4, which is a cubic equation

QUESTION: 13

If x = -2 is a root of equation x^{2} – 4x + K = 0 then value of K is

Solution:

QUESTION: 14

The same value of x satisfies the equations 4x + 5 = 0 and 4x^{2} + (5 + 3p)x + 3p^{2 }= 0, then p is

Solution:

QUESTION: 15

If x = 1 is a root of equation x^{2} – Kx + 5 = 0 then value of K is

Solution:

Root of the equation means that the value when substituted in the equation gives zero as answer.

x^{2 }- kx + 5 = 0

Putting x = 1

1*1 -k + 5 = 0

-k+6=0

k=6

QUESTION: 16

The equation in standard form ax^{2} + bx + c = 0 is written as :

Solution:

We have

Taking LCM,

Multiplying LHS and RHS by x

x^{2}+1=4x

x^{2}-4x+1=0

Which is the required equation.

QUESTION: 17

If x = 1 is a common root of the equation x^{2} + ax – 3 = 0 and bx^{2} – 7x + 2 = 0 then ab =

Solution:

QUESTION: 18

If the area of a rectangle is 24 m^{2} and its perimeter is 20 m, the equation to find its length and breadth would be:

Solution:

QUESTION: 19

If x = 2 is a root of equation x^{2} + 3x – k = 0 then value of k is

Solution:

QUESTION: 20

The roots of the equation

Solution:

x^{2 }- √3x - x + √3 = 0

Taking common x from first two terms

x (x - √3) - 1 (x - √3) = 0

(x - √3) (x - 1) = 0

So, either x = √3 or x = 1

QUESTION: 21

The condition for equation ax^{2} + bx + c = 0 to be quadratic is

Solution:

For ax^{2 }+ bx + c = 0 to be a quadratic equation a0because if a is zero then ax^{2 }= 0 So we are left with only bx + c = 0 which is a linear equation in one variable. So to be a quadratic equation ax^{2} cannot be zero.

QUESTION: 22

The value of q if x = 2 is a solution of 8x^{2} + qx – 4 = 0 is _____

Solution:

QUESTION: 23

The equation in standard form ax^{2} + bx + c = 0 is written as

Solution:

QUESTION: 24

Zeroes of the quadratic polynomial ax^{2} + bx + c and roots of the quadratic equation ax^{2} + bx + c = 0 are ——–

Solution:

Zeros of the polynomial means the value of variable such that the equation is equal to zero.Roots of the equation means the value of the variable for which LHS=RHS which basically means that the equation is equal to zero. Hence Zeros and roots are one and the same thing.

QUESTION: 25

The condition for equation ax^{2} + bx + c = 0 to be linear is

Solution:

QUESTION: 26

The solution of x^{2} + 4x + 4 = 0 is

Solution:

QUESTION: 27

If x^{2} + 2 kx + 4 = 0 has a root x = 2, then the value of k is?

Solution:

QUESTION: 28

Solve 9x^{2} = 36

Solution:

QUESTION: 29

The value/s of x when (x – 4) (3x + 2) = 0 ________

Solution:

QUESTION: 30

The positive root of is

Solution:

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