Question:
If the square of the difference of the zeroes of the quadratic polynomial f(ð‘¥) = ð‘¥2 ð‘ð‘¥ 45 is equal to 144, find the value of p.
Answer:
Given polynomial is x + px + 45
Let the zeroes are a and b
Now, a + b = -p
and a * b = 45
Given, (a - b)2 = 144
=> (a + b)2 - 4 * a * b = 144
=> (-p)2 - 4 * 45 = 144
=> p2 - 180 = 144
=> p2 = 144 + 180
=> p2 = 324
=> p = ±√324
=> p = ±18
So, the value of p is ±18
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