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Quadratic Equations

Question
CBSEENMA10006444
Wired Faculty App

Check whether the following are quadratic equations:
(x – 2) (x + 1) = (x – 1) (x + 3)

Solution

L.H.S. = (x–2) (x + 1)
= x2 – x – 2
R.H.S. = (x – 1) (x + 3)
= x2 + 2x – 3
∴ x2 – x – 2 = x2 + 2x – 3
⇒ – x –2 – 2x + 3 = 0
⇒ – 3x + 1 = 0
∵ It is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation. 

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)

Check whether the following are quadratic equations:
x2 + 3x + 1 = (x – 2)2

Check whether the following are quadratic equations:
(x + 2)3 = 2x(x2 – 1)

Check whether the following are quadratic equations:
x3 – 4x2 – x + 1 = (x – 2)3.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

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

Find the roots of the following quadratic equations by factorisation method:
x2 – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x2 + x – 6 = 0

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