Question

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 1

Step-by-step explanation:

2x2−5x−3=0

2x2−6x+x−3=0

(x−3)(2x+1)=0

x=3,−21

Now,

Zeroes of the polynomial x2−px+q are double in values to the zeroes of polynomial 2x2−5x−3.

Therefore,

Zeroes of polynomial x2−px+q will be- 6,−1

Therefore,

Sum of roots =a−b

6+(−1)=−(−p)

⇒p=5

Product of root =ac

6×−1=q

⇒q=−6

Hence the values of p and q are 5 and −6 respectively.

Answer 2

*Question:—

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.

*Answer:—

→ 2x² − 5x − 3 = 0

→ 2x² − 6x + x − 3 = 0

→ (x−3)(2x+1)=0

→ x = 3 , -1/2

Now,

Zeroes of the polynomial x² − px + q are double in values to the zeroes of polynomial

2x² −5x−3.

Therefore,

Zeroes of polynomial x² − px + q will be −6 ,−1

Therefore,

Sum of roots = -b/a

→ 6 + (−1) = − (−p)

→ p = 6 - 1

→ p = 5

Product of root = c/a

6 × (−1) = q

→ q = −6

Hence,

The values of p and q are 5 and −6 respectively.

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