Question
If α,β are the zeroes of the polynomial x2−px+36 and α2+β2 = 9, then what is the value of p?
Answer: Option D
:
D
Given polynomialx2−px+36
On comparing with the standard form of a quadratic polynomial ax2+bx+c, we get
a = 1, b = -p, c = 36
Here, α and β are the zeroes of the polynomial.
⇒α+β=−ba=p
and αβ=ca=36
Now, α2+β2=(α+β)2 - 2αβ
⇒9=p2−2×36 [∵α2+β2 = 9]
⇒81=p2
⇒p=9or−9
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:
D
Given polynomialx2−px+36
On comparing with the standard form of a quadratic polynomial ax2+bx+c, we get
a = 1, b = -p, c = 36
Here, α and β are the zeroes of the polynomial.
⇒α+β=−ba=p
and αβ=ca=36
Now, α2+β2=(α+β)2 - 2αβ
⇒9=p2−2×36 [∵α2+β2 = 9]
⇒81=p2
⇒p=9or−9
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