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If p and q are zeroes of polynomial x^2 + 2x - 1, find p - q ( x^2 means x square) |
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Answer» Answer: 2√2 Step-by-step explanation: We know, polynomials written in form of x^2 - SX + P refer S as sum of their roots and P as product of their roots. Which, here, in pol. x^2 + 2X - 1 sum of roots = p + q = - 2 product of roots = PQ = - 1 Square on both sides of p + q ⇒ ( p + q )^2 = ( - 2 )^2 ⇒ p^2 + q^2 + 2pq = 4 ⇒ p^2 + q^2 + 2( - 1 ) = 4 ⇒ p^2 + q^2 - 2 = 4 ⇒ p^2 + q^2 = 4 + 2 = 6 Subtract 2pq from both sides ⇒ p^2 + q^2 - 2pq = 6 - 2pq ⇒ ( p - q )^2 = 6 - 2( - 1 ) ⇒ ( p - q )^2 = 6 + 2 = 8 ⇒ p - q = √8 ⇒ p - q = 2√2 |
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