Find the values of k for roots are real and equal in equation:(k + 1)x

1.	Find the values of k for roots are real and equal in equation:(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Answer» The given equation (k +1)x²+ 2(k +3)x + (k +8) = 0 is in the form of ax²+ bx + c = 0 Where a = (k +1), b = 2(k + 3), c = (k + 8) For the equation to have real and equal roots, the condition is D = b²– 4ac = 0 ⇒ (2(k + 3))²– 4(k +1)(k + 8) = 0 ⇒ 4(k +3)²– 4(k² + 9k + 8) = 0 ⇒ (k + 3)²– (k² + 9k + 8) = 0 ⇒ k²+6k + 9 – k² – 9k – 8 = 0 ⇒ -3k + 1 = 0 ⇒ k = \(\frac{1}{3}\) So, the value of k is \(\frac{1}{3}\).

Find the values of k for roots are real and equal in equation:(k + 1)x2 + 2(k + 3)x + (k + 8) = 0

Answer»

The given equation (k +1)x²+ 2(k +3)x + (k +8) = 0 is in the form of ax²+ bx + c = 0

Where a = (k +1), b = 2(k + 3), c = (k + 8)

For the equation to have real and equal roots, the condition is

D = b²– 4ac = 0

⇒ (2(k + 3))²– 4(k +1)(k + 8) = 0

⇒ 4(k +3)²– 4(k² + 9k + 8) = 0

⇒ (k + 3)²– (k² + 9k + 8) = 0

⇒ k²+6k + 9 – k² – 9k – 8 = 0

⇒ -3k + 1 = 0

⇒ k = \(\frac{1}{3}\)

So, the value of k is \(\frac{1}{3}\).