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Question
Write three quadratic polynomials that have no real zeroes.
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Solution
A quadratic polynomial ax2+bx+c=0 has no solution when D=b2−4ac<0
These quadratic polynomials have no zeroesy=2x2−4x+5⇒D=(−4)2−4(2)(5)=16−40=−24y=2x−3x2+2⇒D=(−3)2−4(2)(2)=−7y=x2−2x+4⇒D=(−2)2−4(1)(4)=−12
A quadratic polynomial ax2+bx+c=0 has no solution when D=b2−4ac<0
These quadratic polynomials have no zeroes
y=2x2−4x+5⇒D=(−4)2−4(2)(5)=16−40=−24y=2x−3x2+2⇒D=(−3)2−4(2)(2)=−7
y=x2−2x+4⇒D=(−2)2−4(1)(4)=−12
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