Question

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

Answer 1

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

Answer 2

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