If the square of difference of the zeroes of the quadratic polynomial x2 + px + 45 is equal to 144, then the value of pis If the square of difference of the zeroes of the quadratic polynomial x2 + px + 45 is equal to 144, then the value of pis (a) ± 9 (b) ± 12 (c) ± 15 (d) ± 18
Answers
Given : Square of difference of the zeroes of the quadratic polynomial x²+ px + 45 is equal to 144,
To Find : the value of p
(a) ± 9 (b) ± 12 (c) ± 15 (d) ± 18
Solution:
polynomial ax² + bx + c
sum of zeroes = - b/a
Product of zeroes = c/a
x²+ px + 45
a = 1 , b = p , c = 45
Let say α ,β are zeroes
α + β = -p/1 = -p
αβ = 45/1 = 45
(α - β)² = 144 given
(α - β)² = (α - β)² - 4αβ
=> 144 = (-p)² - 4(45)
=> (-p)² = 324
=> -p = ± 18
value of p is ± 18
Correct option is d) ± 18
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