Question

9.
Which of the following is correct statement ?
A) The equation of degree n has n roots and no more
B) The equation of degree n + 1 has n roots and no more
C) The equation of degree n has n + 1 roots only
D) The equation of degree n + 1 has n roots only
10
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Answer 1

Answer:

A) The equation of degree n has n roots and no more is the correct option

Step-by-step explanation:

Let us take the first statement

The equation of degree n has n roots and no more is the first statement

Let us take a quadratic equation

Here, n = 2

Consider the equation

$x^{2}+2x-3= 0$

To solve this,

$x^{2}+2x-3= 0$

$x^{2}-x+3x -3= 0$

x(x-1)+3(x-1)=0

(x-1)(x+3)=0

x-1= 0 x+3 =0

x=1 x=-3

So, x= 1 , and x=-3 are the roots of the given equation

Here, there are only two roots.

So, n=2 and number of roots is also 2

Similarly in case of a cubic equation where n= 3, number of roots is also 3

So, for any equation with n degree, only n number of roots are present

According to the Fundumental Theorem of Algebra, the degree of an equation is the maximum number of roots possible for the equation

So, the first statement is correct

Considering the Fundumental Theorem of Algebra , the other statements are wrong

Answer 2

Option (A):  the equation of degree n has n roots and no more is correct.

Explanation:

Consider a quadratic equation $(x^2-4) =0$, which has two roots $x=2\ and\ x= -2$. Quadratic equation are the polynomial equations which has highest exponent in variable as 2. All the quadratic equation have 2 roots where roots can be imaginary or real number.

Consider a cubic equation $x^3-6x^2+11x-6=0$, which has three roots $x= 1,x=2\ and\ x=3$.Cubic equation are the polynomial equations which has highest exponent in variable as 3. All the cubic equation has 3 roots where one can be real number and two can be imaginary and vice versa or all three can be real number.

Similarly, we can see this in higher degrees as if the equation has degree 'n' then they will have 'n' roots.

So, Option (A) is correct.