Question

For what value of k the roots of the quadratic equation kx(x-2√5)+10=0 are equal?
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

For equality of roots
b^2-4ac=0
So,20k^2=40k
So,k=2
Please mark as brain list answers

Answer 2

Answer:

Step-by-step explanation:

Given :-

kx(x - 2√5) + 10 = 0

⇒ kx² - 2√5 kx + 10 = 0

Here, a = k, b = - 2√5 and c = 10

Given, roots are equal, then D = b² - 4ac = 0

⇒ (- 2√5k)² - 4 × k × 10 = 0

⇒ 20k² - 40k = 0

⇒ 20k(k - 2) = 0

⇒ k(k - 2) = 0

⇒ k ≠ 0

⇒ k = 2

Hence, the required value of k is 2.

Nature of roots of a quadratic equation :-

(i). If b² - 4ac > 0, the quadratic equation has two distinct real roots.

(ii). If b² - 4ac = 0,  the quadratic equation has two equal real roots.

(iii). If b² - 4ac < 0, the quadratic equation has no real roots.