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For the quadratic equation x² + px + 12 = 0, suppose 4 is one of its roots. If another quadratic x² + px + q = 0 is known to have repeated roots, then what is the value of q?

1. 4
2. 12
3. 3
4. 49/4

Correct answer: 49/4

Solution

Since 4 is a root of x^2+px+12=0: 16+4p+12=0 -> p=-7. For x^2-7x+q=0 to have repeated roots, discriminant 49-4q=0 -> q=49/4.

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