Chapter 6. Quadratic Equations NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers

Chapter 6. QUADRATIC EQUATIONS

Optional Questions and Answers for Algebraic Expressions and Polynomials [1 Mark]

CHECK YOUR PROGRESS 3.1

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Long Questions and Answers for Algebraic Expressions and Polynomials [ 3 or 4 Mark]

CHECK YOUR PROGRESS 6.1

1. Which of the following equations are quadratic equations ?

(i) 3x2+ 5 = x3 + x (ii) 3x2+ 5x + 2 = 0

(iii) (5y+1) (3y-1) = y + 1 (iv) x2+1x+1=52 (v) 3x+2x2 = 5x-4

Solution: (i) 3x2+ 5 = x3 + x

⇒x3+x=3x2+5

⇒x3-3x2+x-5=0 is not a quadratic equation as x3-3x2+x-5 is not a quadratic polynomial.

(ii) 3x2+ 5x + 2 = 0 is a quadratic equation as 3x2+ 5x + 2 is a quadratic polynomial.

(iii) (5y+1) (3y-1) = y + 1

⇒15y2-5y+3y-1=y+1

⇒15y2-2y-1=y+1

⇒15y²-3y-2=0 is a quadratic equation as 15y²-3y-2 is a quadratic Polynomial.

(iv) x2+1x+1=52

⇒2x2+1=5x+1

⇒2x2+2=5x+5

⇒2x2-5x+2-5=0

⇒2x²-5x-3=0 is a quadratic equation as 2x²-5x-3 is a quadratic polynomial .

(v) 3x+2x2 = 5x-4

⇒2x2-5x+3x+4=0

⇒2x2-2x+4=0 is a quadratic equation as 2x2-2x+4 is a quadratic polynomial.

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