if A and B are the zeros of a quadratic polynomial such that a + b equal to 24 and a minus b equal to 8 find the quadratic polynomial having a and b as its zeros
Answers
Answered by
8
Answer:x^2-24x+128
Step-by-step explanation:
As a&b are the zeroes, the quadratic equation will be x ^2-(a+b)x+ab.
Given a+b=24
So a^2+2ab+b^2=576
a^2+b^2=576-2ab
a-b=8
a^2-2ab+b^2=64
a^2+b^2=64+2ab
Equating both equations,
576-2ab=64+2ab
4ab=512
ab=128
The required polynomial is
X ^2-24x+128
Answered by
3
Answer:x^2-24x+128
Step-by-step explanation:
As a&b are the zeroes, the quadratic equation will be x ^2-(a+b)x+ab.
Given a+b=24
So a^2+2ab+b^2=576
a^2+b^2=576-2ab
a-b=8
a^2-2ab+b^2=64
a^2+b^2=64+2ab
Equating both equations,
576-2ab=64+2ab
4ab=512
ab=128
The required polynomial is
X ^2-24x+128
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