Question

find the value of k for which the quadratic equation 4 x square - 3 x + 1 is equals to zero has real and equal roots

Answer 1

yes no k is here..
......
..

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Equation is (k + 4)x²+(k + 1)x + 1 has equal roots.

Here, a = k + 4, b = k + 1, c = 1

D = b²- 4ac.

= (k + 1)² - 4 × (k + 4) × 1

= k² + 1 + 2k - 4k - 16

= k² - 15 - 2k

= k² - 2k - 15

= k² -5k + 3k - 15

= k(k - 5) + 3(k - 5)

⇒ k = - 3 or  5

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.