Question

factorise
${x}^{2} - 2 \sqrt{5} x + 3$
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Answer 1

x^2-2root5x-3

= x² -{(√5 +√2) + (√5 - √2)}x + (√5 - √2)(√5 + √2)

= x² - (√5 + √2)x - (√5 -√2)x + (√5 + √2)(√5 - √2)

= x[x - √5 - √2] - (√5 - √2)[x - √5 - √2]

= [x - √5 - √2][x - √5 + √2]

Hence, x = √5 ± √2 are the zeros of given expression