Question

जाँच कीजिए कि (2x- 1)(x-3) = (x + 5)(x-1) द्विघात समीकरण है।
अथवा
Ams​

Answer 1

Answer:

(2x-1)(x-3)=(x+5)(x-1)

(2x+x)(-1-3)=(x-x)(5-1)

3x(1+3)=(2x+4)

(3x+4)=(2x+4)

x=(3+4)

x=(2+4)

x=7

x=6

7=6

Answer 2

Answer:

The equation is a quadratic equation.

Explanation:

Given the expression,

(2x - 1)(x - 3) = (x + 5)(x - 1)

An algebraic equation in the form of $ax^2 + bx + c = 0$, (where x is a variable, a & b are the coefficients and c is a constant) is said to be a quadratic equation when the variable has highest power 2, and the coefficient of $x^{2}$ is non-zero.    

Opening the brackets on both sides by multiplying each term,  

$2x\times x+2x\times(-3)-1\times x-1\times(-3) = x \times x+ x\times(-1)+5 \times x+ 5\times(-1)$

$2x^{2} -6x- x+3 = x^{2} - x+5 x- 5$

$\implies 2x^{2} -6x- x+3 -x^{2}+ x-5 x+5=0$

$\implies x^{2} -11x+8=0$

The equation has a variable with the highest power 2.

Therefore, the equation is a quadratic equation.