Question

find a quadratic polynomial whose zeroes are -3/2√5 and -1/2. Also, find the zeroes of this polynomial by factorizarion​

Answer 1

AnsWer:-

• Sum of the zeroes = -3/2√5x
• Product of the zeroes = – ½
• p(x) = x2 – (sum of the zeroes) + (product of the zeroes)
• Then, p(x)= x2  -3/2√5x – ½
• p(x)= 2√5x2 – 3x – √5

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Using splitting the middle term method,

⇒ 2√5x² – 3x – √5 = 0

⇒ 2√5x² – (5x – 2x) – √5 = 0

⇒ 2√5x² – 5x + 2x – √5 = 0

⇒ √5x (2x – √5) – (2x – √5) = 0

⇒ (2x – √5)(√5 – 1) = 0

⇒ x = – 1/√5, √5/2

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