Question

If alpha, beta are the roots of the equation 2x square -10x + 5 = 0, then find the value of (alpha + 2) (beta + 2).

Answer 1

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Answer 2

Step-by-step explanation:

Equation: 2x^2 - 10x + 5 = 0

Standard equation is ax^2 + bx + c = 0

Therefore, a= 2 b = - 10. c = 5

Relation between roots and coefficient

Sum:

alpha + beta = - b / a = -(-10)/2 = 10/2 = 5

Product:

alpha x beta = c / a = 5 / 2

question:

(alpha + 2) (beta + 2)

= (alpha x beta) + 2 alpha + 2 beta + 4

= (alpha x beta) + 2 (alpha + beta) + 4

= 5/2 + (2x5) + 4

= 5/2 + 10 + 4. [ now LCM is 2]

= (5+ 20 + 8) / 2

= 33/2