[CIE] [A Level Further Mathematics] Help needed with solving this question EX 1A, #3.
This question is from the Further mathematics book written by lee mckelvey and martin crozier.
Question #3 goes: x^2-(2+p)x+(7+p)=0 has roots that differ by 1. Find the value of p given that p > 0.
I'm unable to solve this problem. At first I did a (alpha) - b (beta) = 1. Which gives me two roots a (alpha) and then a-1 (beta substituted). After doing that I equated a + a -1 = 2+p and then a(a-1) = 7+p. Unfortunately after substitution solving the answer is wrong. Help is appreciated, and please point where in my thought process I got it wrong.
Question #3 goes: x^2-(2+p)x+(7+p)=0 has roots that differ by 1. Find the value of p given that p > 0.
I'm unable to solve this problem. At first I did a (alpha) - b (beta) = 1. Which gives me two roots a (alpha) and then a-1 (beta substituted). After doing that I equated a + a -1 = 2+p and then a(a-1) = 7+p. Unfortunately after substitution solving the answer is wrong. Help is appreciated, and please point where in my thought process I got it wrong.
NEVERMINDDDD I'm so dumb! I managed to solve it successfully. It was an error with a(a-1) = 7+p, where my final eqn was supposed to be 2a-3 but I wrote 3-2a instead. XD
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