Check whether (x – 2)(x + 1) = (x – 1)(x + 3) is quadratic equation ?

byAmlesh Mahato •January 22, 2021

The Biotic World is the best free Educational Website for Students. The Biotic World Provides NCERT Solution PDF, CBSE Notes PDF, NCERT Books PDF for class 8, 9, 10, 11, 12. The Biotic World also provides GU TDC Syllabus, Previous Years Question Papers, TDC notes on different topics of Physics, Chemistry, Mathematics, Zoology and Botany any many more. So, Follow us to get tuned with latest updates.

Solution:

(x – 2)(x + 1) = (x – 1)(x + 3)

$\large \Rightarrow x(x+1)-2(x+1)=x(x+3-1(x+3)$

$\large \Rightarrow x(x+1)-2(x+1)=x(x+3-1(x+3)$

$\large \Rightarrow x(x+1)-2(x+1)=x(x+3)-1(x+3)$

$\large \Rightarrow x^2+x-2x-2=x^2+3x-x-3$

$\large \Rightarrow x^2-x^2+x-2x-3x+x-2+3=0$

$\large \Rightarrow -3x-2+3=0$

$\large \Rightarrow -3x+1=0$

No, Do not match the Quadratic Equation Format.

∵ $\large ax^{2}+bx+c=0$

Exercise 4.1

1. Check whether the following are quadratic equations :

(i) $\large (x + 1)^2=2(x-3)$

(ii) $\large x^2-2x=(-2)(3-x)$

(iii) (x – 2)(x + 1) = (x – 1)(x + 3)

(iv) (x – 3)(2x +1) = x(x + 5)

(v) (2x – 1)(x – 3) = (x + 5)(x – 1)

(vi) $\large x^2+3x+1=(x-2)^2$

(vii) $\large (x+2)^3=2x(x^2-1)$

(viii) $\large x^3-4x^2-x+1=(x-2)^3$

2. Represent the following situations in the form of quadratic equations :

(i) The area of a rectangular plot is 528 m2 . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

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

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been8 km/h less, then it would have taken 3 hours more to cover the same distance. Weneed to find the speed of the train.

Tags: Chapter-4 Exercise-4.1 Math- Class 10