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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!
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