if alpha and beta are the zeroes of the equation X sq. -5x + 6 =0 find the value of alpha sq. – beta sq.​

2 thoughts on “if alpha and beta are the zeroes of the equation X sq. -5x + 6 =0 find the value of alpha sq. – beta sq.​”

1. Answer:

   (alpha)^2-(beta)^2=+5or-5

   Step-by-step explanation:

   x^2-5x+6=0

   x^2-2x-3+6=0

   x(x-2)-3(x-2)=0

   (x-2)(x-3)=0

   x-2=0=>x=2

   x-3=0=>x=3

   therefore alpha=2 and beta=3

   (alpha)^2-(beta)^2=2^2-3^2=4-9=-5

   (OR)

   x^2-5x+6=0

   x^2-3x+2x+6=0

   x(x-3)-2(x-3)=0

   (x-3)(x-2)=0

   x-3=0=>x=3

   x-2=0=>x=2

   therefore alpha=3 and beta=2

   (alpha)^2-(beta)^2=3^2-2^2=9-4=5

   therefore (alpha)^2-(beta)^2=+5 or -5

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2. Step-by-step explanation:

   x²-5x+6=0

   alpha + beta = -b/a = -(-5)/1 = 5

   alpha × beta = c/a = 6/1 = 6

   (alpha + beta)² = alpha² + beta² + 2×aplha×beta

   (5)²= alpha² + beta² + 2×6

   alpha² + beta² = 25-12 = 13

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