Find the roots of the given quadratic equation

1. (x + 1)^{2} = 2(x – 3)

2. 100 x^{2} – 20x + 1 = 0

Maths

Class 9

709

Advika

Ethan

Answer / Solution

Answer / Solution

Answer 1 To solve the quadratic equation of the following equation

x^{2} – 3x – 10 = 0

⇒ x^{2} – 5x + 2x + 10 = 0

⇒ x(x – 5) + 2(x – 5) = 0

⇒ (x – 5)(x + 2) = 0

⇒ (x – 5) = 0 or (x + 2) = 0

i.e. x = 5 or x = -2

Therefore, the roots of the quadratic equation x^{2} – 3x – 10 = 0 is 5 and –2.

Answer 2: After solving the quadratic equation 100 x^{2} – 20x + 1 = 0 we get

100 x^{2} – (10 + 10)x + 1 = 0

100 x^{2} – 10x – 10x + 1 = 0

10x (10x – 1) – 1 (10x – 1) = 0

(10x – 1) – 1 (10x – 1) = 0

Either x = 1/10 or x = 1/10, Hence, the roots of the given 100 x^{2} – (10 + 10)x + 1 = 0 are 1\10 and 1/10

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