If x 2 + 2ax + 10 - 3a > 0 for all x ∈ R, then

If x<sup>2</sup> + 2ax + 10 - 3a > 0 for... - Solved

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Question 35

Mathematics Linear and Quadratic Equations Hard

If x<sup>2</sup> + 2ax + 10 - 3a > 0 for all x ∈ R, then

(A) - 5 < a < 2

(B) a < -5

(C) a > 5

(D) 2 < a < 5

✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Given equation: \[ x^2 + 2ax + 10 - 3a > 0 \] According to the given condition, we have: \[ 4a^2 - 4(10 - 3a) < 0 \] \[ \Rightarrow a^2 + 3a - 10 < 0 \] \[ \Rightarrow (a + 5)(a - 2) < 0 \] \[ \Rightarrow -5 < a < 2 \]

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