A and b are roots of the equation 2x^2 +5x - 4. Calculate the value of (a - b)^2?

a + b = -5/2
ab = -4/2

1 Answer
salamat
Sep 6, 2017

14 1/41414

Explanation:

Sum of roots, SoR = a + b = -5/2=a+b=−52

Product of roots, PoR = a*b = -4/2 =-2=a⋅b=−42=−2

(a - b)^2 = a^2 + b^2 - 2ab(a−b)2=a2+b2−2ab->i→i

from
(a + b)^2 = a^2 + b^2 + 2ab(a+b)2=a2+b2+2ab, therefore
(a + b)^2 - 2ab = a^2 + b^2(a+b)2−2ab=a2+b2->a→a

plug in aa into ii
(a - b)^2 = (a + b)^2 - 2ab - 2ab(a−b)2=(a+b)2−2ab−2ab
(a - b)^2 = (a + b)^2 - 4ab(a−b)2=(a+b)2−4ab

Plug in values of SoR & PoR in above equation.
(a - b)^2 = (-5/2)^2 - 4(-2) = 25/4 + 8 = 14 1/4(a−b)2=(−52)2−4(−2)=254+8=1414

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