The quadratic polynomial p X with-2_ and 4 as a product and one of the zeroes respectively.
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The quadratic polynomial p X with-2_ and 4 as a product and one of the zeroes respectivelyGiven: Product of zeroes =−81, and one of the zeroes =3
Let the zeroes of the quadratic polynomial be α,β
Let β=3, and given αβ=−81⟹α=
3
−81
=−27
So, the other zero of the polynomial is −27
Also, the sum of the zeroes of the polynomial =−27+3=−24
So the expression of required polynomial p(x) is given by:
x
2
−(sum of the zeroes of the polynomial)x+(product of the zeroes)
⇒p(x)=x
2
−(−24)x+(−81)
⇒p(x)=x
2
+24x−81
Therefore, the quadratic polynomial p(x) is x
2
+24x−81
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