RS Aggarwal Class 10 Solutions Quadratic Equations Exercise 10A

Question 1:

(i) x2-x+3=0 is a quadratic polynomial.

∴ x2-x+3=0 is a quadratic equation.

(ii) 2x2+ [latex]\frac { 5 }{ 2 } [/latex]x-√3=0

⇒ 4x2+5x-2√3=0

Clearly is 4x2+5x-2√3=0 a quadratic polynomial.

∴ 2x2+ [latex]\frac { 5 }{ 2 } [/latex]x-√3=0 is a quadratic equation.

(iii) √2x2+7x+5√2=0 is a quadratic polynomial.

∴ √2x2+7x+5√2=0 is a quadratic equation.

(iv)[latex]\frac { 1 }{ 3 } [/latex]x2+[latex]\frac { 1 }{ 5 } [/latex]x-2=0

⇒ 5x2+3x-2=0

Clearly, 5x2+3x-2=0 is a quadratic equation.

[latex]\frac { 1 }{ 3 } [/latex]x2+[latex]\frac { 1 }{ 5 } [/latex] is a quadratic equation.

(v) x2-3x-√x+4=0 is not a quadratic polynomial since it contains √x, in which power 1/2 of x is not an integer.

∴ x2-3x-√x+4=0 is not a quadratic equation.

(vi) x-[latex]\frac { 6}{ x } [/latex]=3

⇒ x2-3x-6 =0

And (x2-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.

Hence, x-[latex]\frac { 6}{ x } [/latex]=3 is a quadratic equation.

(vii) x+[latex]\frac { 2}{ x } [/latex]= x2

⇒ x3-x2-2 =0

And (x3-x2-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.

Hence, x+[latex]\frac { 2}{ x } [/latex]= x2 is not a quadratic equation.

(viii) [latex]{ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } =5 [/latex] ⇒ x4 -1=5x2

⇒x4-5x2-1 =0

And (x4-5x2-1 =0) being a polynomial of degree 4.

Hence [latex]{ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } =5 [/latex] is not a quadratic equation.