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 1

Appropriate 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.

Answers:

• p → -5 and q → -6.

Step-by-step Explanation:

Given that :

• The zeroes of the polynomial are → x² + px + q.
• x² + px + q are double in value to the zeroes of → 2x² – 5x – 3.

To Find :

• The value of p and q.

Formula Used :

• Sum of roots → - b/a.
• Product of roots → c/a.

Finding the value of p and q :

Zeroes of 2x² – 5x – 3.

ㅤㅤ→ 2x² - 5x - 3.

ㅤㅤ→ 2x² - 6x + x - 3.

ㅤㅤ→ 2x (x - 3) + 1 (x - 3).

ㅤㅤ→ (x - 3) (2x + 1).

.°. Zeroes of 2x² – 5x – 3 are 3 and - 1/2.

A.T.Q.

• Zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² – 5x – 3.

.°. Zeroes are -1 and 6.

On substituting the known values, we get.

ㅤㅤ→ Sum of roots → - b/a.

ㅤㅤ→ 6 + (- 1) → - p.

ㅤㅤ→ p → - 5.

On substituting the known values, we get.

ㅤㅤ→ Product of roots → c/a.

ㅤㅤ→ 6 (- 1) → q

ㅤㅤ→ q → - 6.

.°. The values of :

• p → - 5.
• q → - 6.