Solve for x in the quadratic equation. 2x2 + 12x + 10 = 0

Step 1: Analyze the question We need to find the values of x that satisfy 2x² + 12x + 10 = 0.

Step 2: Concept For a quadratic equation, first simplify by dividing out any common factor. Then factorise (find two numbers whose product is the constant term and whose sum is the coefficient of x).

Step 3: Solution

Divide every term by 2:

x² + 6x + 5 = 0

We need two numbers that multiply to +5 and add to +6. These are 5 and 1.

(x + 5)(x + 1) = 0

So:

• x + 5 = 0 → x = -5
• x + 1 = 0 → x = -1

Check:

• x = -5: 2(25) + 12(-5) + 10 = 50 - 60 + 10 = 0 ✓
• x = -1: 2(1) + 12(-1) + 10 = 2 - 12 + 10 = 0 ✓

Step 4: Answer x = -5, -1, which is option A.

Why the other options fail:

• B (-5, 1): x = 1 gives 2 + 12 + 10 = 24, not 0.
• C (-3, -2): the product is 6, not 5.
• D and E: positive roots can't work because all the coefficients are positive, so the sum would never be zero.

Tip: When all the coefficients of a quadratic are positive, both roots must be negative. This quickly rules out options D and E. Also, always check for a common factor first, because it makes the factorising much easier.