On multiplying the polynomials x2 + px + q and x2 + mx + n with each other, we get a polynomial whose zeroes are 1, 2, 3 and 4. What will be the value of (p + m)(q + n)?
Solution
Correct Answer: Option E
Here, p, m, q and n could attain different values in different cases. For example, if x2 + px + q correspond to roots 1 and 2, and x2 + mx + n correspond to roots 3 and 4, then p = -3, q = 2, m = -7, n = 12. Here, (p + m)(q + n) = (-10)(14) = -140. And, if x2 + px + q correspond to roots 1 and 3, and x2 + mx + n correspond to roots 2 and 4, then p = -4, q = 3, m = -6, n = 8. Here, (p + m)(q + n) = (-10)(11) = -110.
We see that unique value of (p + m)(q + n) cannot be determined.
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