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#### has            (A) four real roots                                 (B) two real roots            (C) no real roots                                    (D) one real root.

(C) no real roots

Solution

Here the given equation is

[using? ]

Put

Compare with where

Here    a=1,b=1,c=1

Here the given equation has no real roots.

#### Which of the following equations has no real roots ?

(A)

Solution

We know that if the equation has no real roots, then

(A)

Compare with  where

Here
(no real roots)

(B)

Compare with  where

Here
(two distinct real roots)

(C)

Compare with  where

Here
(two distinct real roots)

(D)

Compare with  where

Here
(two equal real roots)

Here only  has no real rots.

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• HD Video Lectures
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• Faculty Support #### Which of the following equations has two distinct real roots?

We know that if roots are distinct and real, then

Here only option (B)  have two distinct real roots.

#### The quadratic equation  has(A) two distinct real roots                                 (B) two equal real roots(C) no real roots                                                (D) more than 2 real roots

(C) no real roots

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• Faculty Support #### Which constant must be added and subtracted to solve the quadratic equation  by the method of completing the square?

Here the given quadratic equation is

So

#### Values of k for which the quadratic equation  has equal roots is(A) 0 only         (B) 4                (C) 8 only         (D) 0, 8

(D) 0, 8

Here the given equation is

Compare with  where

a=2,b=-k,c=k

It is given that roots are equal.

Hence

Hence for the value of k = 0, 8 the equation  has equal roots.

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• Faculty Support #### Which of the following equations has the sum of its roots as 3?

(B)

If  is a quadratic equation the sum of its roots are

(A)

Here b=-3,a=2

Sum of its roots =

(B)

Here b=-3,a=3

Sum of its roots =

(C)

Here

Sum of its roots =

(D)

Here b=-3,a=3

Sum of its roots

Hence only B has sum of its roots 3

#### If  is a root of the equation , then the value of k is

(A) 2

Solution

As we know that if  is a root of the equation  then  should satisfy its equation.

Put

Hence value of k is 2.

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• Faculty Support #### Which of the following equations has 2 as a root ?

(C)

Solution

(A)

Put       x = 2

(B)

(C)

(D)

Hence option (C) is only satisfy x = 2.

Hence C has 2 as a root.

#### Which of the following is not a quadratic equation?

Quadratic equation: A quadratic equation in x is an equation that can be written in the standard form ,

Where a, b and c are real numbers

[using (a – b)2 = a2 + b2 – 2ab]

It is a quadratic equation because it is in the form

(B)

It is a quadratic equation because it is in the form

(C)

It is not in the form of

Hence it is not a quadratic equation.

(D)

It is in the form of

Hence it is a quadratic equation

Only option (C) is not in the form of

Hence (C) is not a quadratic equation.  