Mathematics · Quadratic Equations · NCERT Exercises

Exercise 4.1

Complete, independently verified solutions for NCERT Exercise 4.1.

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Mathematics · Chapter 4 · NCERT Exercises

Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

Question

Question 1

quadratic equations · standard form

Check whether the following are quadratic equations.

$(x+1)^2=2(x-3)$
$x^2-2x=(-2)(3-x)$
$(x-2)(x+1)=(x-1)(x+3)$
$(x-3)(2x+1)=x(x+5)$
$(2x-1)(x-3)=(x+5)(x-1)$
$x^2+3x+1=(x-2)^2$
$(x+2)^3=2x(x^2-1)$
$x^3-4x^2-x+1=(x-2)^3$

Solution

$x^2+7=0$
Quadratic.
$x^2-4x+6=0$
Quadratic.
$x^2-x-2=x^2+2x-3\Rightarrow3x-1=0$
Not quadratic.
$2x^2-5x-3=x^2+5x\Rightarrow x^2-10x-3=0$
Quadratic.
$2x^2-7x+3=x^2+4x-5\Rightarrow x^2-11x+8=0$
Quadratic.
$x^2+3x+1=x^2-4x+4\Rightarrow7x-3=0$
Not quadratic.
$x^3+6x^2+12x+8=2x^3-2x\Rightarrow x^3-6x^2-14x-8=0$
Not quadratic.
$x^3-4x^2-x+1=x^3-6x^2+12x-8\Rightarrow2x^2-13x+9=0$
Quadratic.

Question

Question 2

forming quadratic equations · word problems

Represent each situation as a quadratic equation.

A rectangular plot has area 528 m² and length one metre more than twice its breadth.
The product of two consecutive positive integers is 306.
Rohan’s mother is 26 years older than him; the product of their ages three years from now is 360.
A train covers 480 km. At 8 km/h less, it would take 3 hours longer.

Solution

Let breadth = x m, length = 2x + 1 m.
$x(2x+1)=528\Rightarrow2x^2+x-528=0$
Let the integers be x and x + 1.
$x(x+1)=306\Rightarrow x^2+x-306=0$
Let Rohan’s present age be x years; his mother is x + 26.
$(x+3)(x+29)=360\Rightarrow x^2+32x-273=0$
Let the speed be x km/h.
$\frac{480}{x-8}=\frac{480}{x}+3$
$x^2-8x-1280=0$