Question

(c) If the two roots of the equation 3x2 + 12x = 2p(x-6) are equal and
opposite in sign, then find the product of the roots.​

Answer 1

Given info : If the two roots of the equation 3x² + 12x = 2p (x-6) are equal and opposite in sign.

To find : The product of the roots is ..

solution : roots of quadratic equation, 3x² + 12x = 2p(x - 6) are equal and opposite in sign.

so, sum of roots = 0

⇒sum of roots = - coefficient of x/coefficient of x²

first rearrange equation,

3x² + 12x = 2p(x - 6)

⇒3x² + 12x - 2px + 12p = 0

⇒3x² + (12 - 2p)x + 12p = 0

so, sum of roots = -(12 - 2p)/3 = 0

⇒p = 6

now product of roots = constant/coefficient of x²

= 12p/3

= 12 × 6/3

= 24

There the product of roots is 24.

Answer 2

Answer:

For your information the 1st ans has a fault(in sign). Just think naturally, if two roots are opposite in sign their product must be -ve.

The correct ans will be -24. (VERIFIED ANSWER)