Question

if x=-2 is a root of the equation 3x2+7x+p=0,find the values of k,so that the roots of the equation x2+k[4x+k-1[+p=0 are equal

Answer 1

Here, x = – 2 is the root of the equation

3x^2 + 7x + p = 0

⇒ 3(– 2)2 + 7(– 2) + p = 0

⇒ p = 2

Root of the equation x^2 + 4kx + k^2 – k + 2 = 0  are equal.

⇒ b^2 – 4ac = 0

⇒ 16k^2 – 4(k^2 – k + 2) = 0

⇒ 3k^2 + k – 2 = 0

⇒ (3k – 2)(k + 1) = 0

⇒ k =  2  ÷ 3  , − 1

Answer 2

Step-by-step explanation:

According to the Question

x = - 2

3x^2 + 7x + p = 0

⇒ 3(- 2)^2 + 7(- 2) + p = 0

⇒ p = 2

Now apply the formula of discriminant :-

⇒ b^2 - 4ac = 0

⇒ 16k^2 - 4(k^2 - k + 2) = 0

⇒ 3k^2 + k - 2 = 0

⇒ (3k - 2)(k + 1) = 0

⇒ k =  $\bf\huge\frac{2}{3}$  and − 1