Question

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Answer 1

Answer:

Option(C)

Step-by-step explanation:

Given Equations are:

(i) x² + px + q = 0

(ii) x³ + 3x² + 5x + 3 = 0

Substitute x = -1 in (ii), we get

⇒ (-1)³ + 3(-1)² + 5(-1) + 3

⇒ -1 + 3 - 5 + 3

⇒ 0.

∴ x = -1 satisfy the equation (ii), therefore one root of the equation is -1.

Let the two common roots be α,β.

(1)

From Equation (i), we get

α + β = -p   ----- (iii)

From equation (ii), we get

⇒ α + β = -3

⇒ α + β - 1 = -3

⇒ α + β = -2   ---- (iv)

On solving (iii) & (iv), we get

⇒ -p = -2

⇒ p = 2

(2)

From equation (i), we get

αβ = c/a

αβ = q     ------ (iv)

From equation (ii), we get

αβ = -3      -------- (v)

on solving (iv) & (v), we get

⇒ q = -3

The minimum value of p + q is:

⇒ 2 - 3

⇒ - 1.

∴ Minimum value of p + q is - 1.

Hope it helps!