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in Quadratic Equations by (56.3k points)

If 2 is a root of the quadratic equation 3x2 + px -8 = 0 and the quadratic equation 4x2 – 2px + k = 0 has equal roots, find the value of k.

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Given,

2 is as root of 3x2 + px -8 = 0

So, on substituting x = 2 the LHS will become zero and satisfy the equation.

⇒ 3(2)2 + p(2) – 8 = 0

⇒ 12 + 2p – 8 = 0

⇒ 4 + 2p = 0

⇒ p = -2

Now, substituting the value of p in the second equation we have

4x2 – 2(-2)x + k = 0

⇒ 4x+ 4x + k = 0

It’s given that the above equation has equal roots.

Thus the discriminant, D = 0

The equation 4x+ 4x + k = 0 is in the form of ax+ bx + c = 0

Where a = 4, b = 4, c = k

D = b2 – 4ac

⇒ 42 – 4(4)(k) = 0

⇒ 16 – 16k = 0 [dividing by 16 both sides]

⇒ k = 1

Therefore, the value of k is 1.

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