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

Answer

R.H.S. = (x – 2)2 = x2 – 4x + 4
∴ x2 + 3x + 1 = x2 –4x + 4
⇒ 3x + 4x + 1 – 4 = 0
⇒ 7x – 3 = 0
∵ It is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation. 

 

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Some More Questions From Quadratic Equations Chapter

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

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.