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Quadratic Equations

Question
CBSEENMA10006443
Wired Faculty App

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

Solution

R.H.S. = (–2) (3 – x) = – 6 + 2x
∴ x2 – 2x = – 6 + 2x
⇒ x2 – 2x + 6 – 2x = 0
⇒ x2 – 4x + 6 = 0
∵ It is of the form ax2 + bx + c = 0 where a = 1,b = –4, c = 6.
Hence, the given equation is a quadratic equation.

Some More Questions From Quadratic Equations Chapter

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

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

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