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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

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For a quadratic equation, ax2 + bx + c = 0, 

D = b2 – 4ac 

If D = 0, roots are equal 

Given, 

2 is a root of the quadratic equation 3x2 + px - 8 = 0

⇒ 3 × 4 + 2p – 8 = 0 

⇒ 2p = -4 

⇒ p = -2

Now, 

the quadratic equation 4x2 - 2px + k = 0 has equal roots

⇒ 4x2 + 4x + k = 0 has equal roots 

⇒ D = 16 – 16k = 0 

⇒ k = 1

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