If the roots of the equation x2 + kx + 143 = 0 are two successive odd natural numbers, then find the value of p.
Explanation:
We know the product of roots in a quadratic equation = c/a
Since the roots are consecutive natural numbers, hence the product of these consecutive natural numbers = 143.
Let the first root be a – 1 and the other root will be a + 1.
∴ (a - 1)(a + 1) = 143
⇒ a2 – 1 = 143
⇒ a2 = 144
⇒ a = ± 12
We will reject a = -12 as a is a natural number.
∴ a = 12
⇒ The roots are 12 – 1 = 11 and 12 + 1 = 13.
∴ Sum of the roots = 11 + 13 = 24 = -k
⇒ k = -24
Hence, option (b).
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