The polynomial with roots negative square root of 5, square root of 5, and 3 is Option (C) - 3
-5x +15 = 0 .
In the above question, it is given that a polynomial with roots negative square root of 5, square root of 5, and 3
=> α =
β =
ω = 3
We need to find the polynomial which can be made using the given roots of the polynomial
We know that, a cubic polynomial can be formed with the help of given roots as following
- ( α+β+ω)
+ (αβ+βω + αω)x - (αβω) = 0
So, first we'll find,
Sum of roots = α+β+ω = +
+ 3 = 3
Product of two roots at a time = αβ+βω + αω = +
3 + 3.
=
-5 +
= -5
Product of roots = αβω = = -15
Now putting all the values in the polynomial equation, we get
- ( α+β+ω)
+ (αβ+βω + αω)x - (αβω) = 0
- ( 3)
+ (-5 )x - (-15) = 0
- 3
+ (-5 )x - (-15) = 0
- 3
-5x +15 = 0
Hence, the polynomial with roots negative square root of 5, square root of 5, and 3 is - 3
-5x +15 = 0 .
To learn more about, cubic polynomial, here
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