Rotational symmetry:- When an object is rotated about the center by a number of degrees and the object appears to be the same. It is known as the rotational symmetry of the object.The order of symmetry is the number of positions the object looks the same in a $360^{\circ}$ rotation.The ... Read More

When a figure is folded in half, along its line of symmetry, both the halves match each other exactly. This line of symmetry is called the axis of symmetry. $(a)$. An equilateral triangle has three lines of symmetry.$(b)$. An isosceles triangle has one line of symmetry.$(c)$. A scalene triangle has no line of symmetry.$(d)$. A square has four lines ... Read More

To do:We have to find which of the given polynomials is of one variable and which are not and state the reasons.Solution:(i) In $4x^2−3x+7$, All the powers of $x$ are whole numbers.Therefore, it is a polynomial in one variable $x$.(ii) In $y^2+\sqrt2$The power of $y$ is a whole number.Therefore, it ... Read More

To do :We have to find the coefficient of $x^2$ in each of the given expressions.Solution :Coefficient :A coefficient is the numerical part of a product of numbers and variables.Therefore, (i) \( 2+x^{2}+x \)$x^{2}+x+2$ can be written as $1\times x^2+1\times x+2$Here, $x^2$ is multiplied by $1$.Therefore, the coefficient of $x^2$ ... Read More

 To do:We have to write the degree of each of the given polynomials.Solution:Degree of a polynomial:A polynomial's degree is the highest or the greatest power of a variable in a polynomial.Therefore, (i) In $5 x^{3}+4 x^{2}+7 x^1$, the term $5x^3$ has a variable of power $3$, the term $4x^2$ has ... Read More

To do: We have to classify the given polynomials as linear, quadratic and cubic polynomials.Solution: Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.A linear polynomial is a polynomial of degree 1.A quadratic polynomial is a polynomial of degree 2.A cubic polynomial ... Read More

To do: We have to find the value of the polynomial \( 5 x-4 x^{2}+3 \) at(i) \( x=0 \)(ii) \( x=-1 \)(iii) \( x=2 \)Solution:To find the value of the polynomial $f(x)$ at $x=a$, we have to substitute $x=a$ in $f(x)$.Let $f(x)=5 x-4 x^{2}+3$Therefore, (i) When $x=0$, $f(0) = 5 ... Read More

To do: We have to find \( p(0), p(1) \) and \( p(2) \) for each of the given polynomials.Solution:To find the value of the polynomial $f(x)$ at $x=a$, we have to substitute $x=a$ in $f(x)$.Therefore, (i) \( p(y)=y^{2}-y+1 \)$p(0) = (0)^{2}-(0)+1$$= 0-0+1$$= 1$$p(1) = (1)^{2}-(1)+1$$= 1-1+1$$= 1$$p(2) = (2)^{2}-(2)+1$$= 4-2+1$$= ... Read More

To do:We have to verify whether the given values are zeroes of the given polynomials. Solution:The zero of the polynomial is defined as any real value of $x$, for which the value of the polynomial becomes zero.Therefore, (i) \( p(x)=3 x+1, x=-\frac{1}{3} \)$p(-\frac{1}{3})=3(-\frac{1}{3})+1$$=-1+1$$=0$Therefore, $x=-\frac{1}{3}$ is the zero of the polynomial $p(x)=3 ... Read More

To do:We have to find the zeroes of the given polynomials.Solution :The zero of a polynomial is defined as any real value of $x$, for which the value of the polynomial becomes zero.Therefore, (i) Zero of the polynomial $p(x) = x+5$ is, $x+5 = 0$$x = -5$.Zero of the polynomial ... Read More