Q1 of 58 Page 106

Check whether the following are quadratic equation:

x3 - 4x2 - x + 1 = (x - 2)3

x3 - 4x2 - x + 1 = (x - 2)3

RHS = (x - 2)3 = x3 - 23 - 3 × x × 2(x - 2)


(∵(a + b)3 = a3 + b3 + 3ab(a + b))


= x3 - 8 - 6x2 + 12x


Equating LHS and RHS


x3 - 4x2 –x + 1 = x3 - 8 - 6x2 + 12x


2x2 - 13x + 9 = 0


which is of the form ax2 + bx + c = 0


∴ it is a quadratic equation.


More from this chapter

All 58 →
1

Check whether the following are quadratic equation:

x2 + 3x + 1 = (x - 2)2

 1

Check whether the following are quadratic equation:

(x + 2)3 = 2x(x2 - 1)

 2

Represent the following situations in the form of quadratic equation:

The area of a rectangular plot is 528m2. The length of the plot is one meter more than twice its breadth. We need to find the length and breadth of the plot.

 2

Represent the following situations in the form of quadratic equation:

The product of two consecutive positive integers is 306. We need to find the integers.