Q20 of 47 Page 1

Solve the equation for x.

Given equation,

⇒

Cross multiplying, we get

⇒ 5x + 15 = (11 - x) (x + 1)

⇒ 5x + 15 = 11x – x² + 11 – x

⇒ 5x + 15 – 11x + x² – 11 + x = 0

⇒ x² – 5x + 4 = 0

By factorization method,

⇒ x² - x – 4x + 4 = 0

⇒ x (x - 1) – 4 ( x - 1) = 0

⇒ (x - 1) (x – 4) = 0

⇒ x - 1 = 0 (or) x - 4 = 0

⇒ x = 1 (or) x = 4

The solution of the given equation is x = 1, 4.

If the points are collinear and 2b + c = 4, find the values of b and c.

If the point is equidistant from the points and , find k. Also, find the length of AP.

Find the value of p for which the quadratic equation = 0 has equal roots. Also, find these roots.

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is:

(i) an odd number

(ii) a perfect square number

(iii) divisible by 5

(iv) a prime number less than 20