Multiple choice

What is the respective ratio of negative value of sum of squares of roots to the product of the roots of the equation 7x2 + 12x + 18 = 0 ? समीकरण 7x2 + 12x + 18 = 0 के मूलों के वर्गो के योगफल के ऋणात्मक का मूलों के गुणनफल से क्रमशः क्या अनुपात है?

  1. 6 : 1

  2. 1 : 6

  3. 6 : 7

  4. 7 : 6

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For ax² + bx + c = 0: sum of roots = -b/a, product = c/a. Sum of squares = (sum)² - 2(product) = (b²/a²) - (2c/a). For 7x² + 12x + 18 = 0: sum = -12/7, product = 18/7. Sum of squares = (144/49) - (36/7) = (144-252)/49 = -108/49. Negative value of sum of squares = 108/49. Ratio = (108/49) / (18/7) = (108/49) × (7/18) = 6/7. Option A incorrectly uses reciprocal. Option B inverts the correct ratio. Option D swaps numerator and denominator.