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# let alpha beta roots x x then equation

let alpha beta roots x x then equation
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You need to remember how to use the roots to form a quadratic equation such that:`x^2 – sx + p = 0`Since s expresses the sum of roots and p expresses the product of roots, hence you may form the equation that has the roots `alpha + 3 ` and `beta + 3`  such that:`x^2 – (alpha + 3 + beta + 3)x + (alpha + 3)(beta + 3) = 0`You need to open the brackets such that:`x^2 – (alpha + beta + 6)x + (alpha*beta + 3(alpha + beta) + 9) = 0`You need to use Vieta’s formulas for the first equation  `2x^2-15x+4 = 0`  to relate the coefficients of quadratic to its sum and product of roots such that:`alpha + beta = 15/2“alpha*beta = 4/2 = 2`You should substitute `15/2`  for `alpha + beta ` and 2 for `alpha*beta ` in equation `x^2 – (alpha + beta + 6)x + (alpha*beta + 3(alpha + beta) + 9) = 0`  such that:`x^2 – (15/2 + 6)x + (2 + 3(15/2) + 9) = 0“x^2 – 27/2x + 67/2 = 0“2x^2 – 27x + 67 = 0`Hence, evaluating the quadratic equation that has the roots `alpha + 3`  and `beta + 3` , under given conditions, yields `2x^2 – 27x + 67 = 0.`
let alpha beta roots x x then equation