If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of 2x2 – 5x – 3, find the value of p and q.
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Answer:
2x
2
−5x−3=0
2x
2
−6x+x−3=0
(x−3)(2x+1)=0
x=3,−
2
1
Now,
Zeroes of the polynomial x
2
−px+q are double in values to the zeroes of polynomial 2x
2
−5x−3.
Therefore,
Zeroes of polynomial x
2
−px+q will be- 6,−1
Therefore,
Sum of roots =
a
−b
6+(−1)=−(−p)
⇒p=5
Product of root =
a
c
6×−1=q
⇒q=−6
Hence the values of p and q are 5 and −6 respectively.
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