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3 Find the quadratic polynom with variablex whose Zeroes core 1 and 2 and whoseprime-coefficient is-5. |
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Answer» hey Step-by-step explanation: Let the zeroes of the quadratic polynomial be α=1,β=−3 Then, α+β=1+(−3)=−2 αβ=1×(−3)=−3 Sum of zeroes =α+β=−2 Product of zeroes =αβ=−3 Then, the quadratic polynomial =x 2 −( sum of zeroes )x+ product of zeroes =x 2 −(−2)x+(−3)=x 2 +2x−3 Verification: Sum of zeroes =α+β=1+(−3)=−2 or =− COEFFICIENT of x 2
Coefficient of x =− 1 (2) =−2 Product of zeroes =αβ=(1)(−3)=−3 or = Coefficient of x 2
CONSTANT term = 1 −3 =−3 So, the relationship between the zeroes and the coefficients is verified. |
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