1.

Find the value of 'y' in the equation x2 - 11x + y = 0 if 3a - 2b = 8 where a and b are the roots of the equation.1. 282. 303. 244. 32

Answer» Correct Answer - Option 2 : 30

Concept:

For an equation ax2 + bx +c = 0

  • Sum of the roots = \(\rm-b\over a\)
  • Product of the roots = \(\rm c\over a\)
  • Roots of the equation = \(\rm x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
  • If α and β are the roots of the equation the equation can be represented as (x - α)(x - β) = 0

The roots of a quadratic equation ax2 +bx + c = 0 are real if:

b2 - 4ac ≥ 0

Calculation:

For a and b are the roots of x2 - 11x + y = 0 then, 

a + b = 11 and ab = y

⇒ b = 11 - a

Given 3a - 2b = 8

⇒ 3a - 2(11 - a) = 8

⇒ 5a - 22 = 8 

⇒ 5a = 30

⇒ a = 6

As b = 11 - a = 5

Now ab = y 

⇒ y = 6 × 5

⇒ y = 30


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