Question

Give any 2 example s for quadratic polynomial s which are not having real roots

Answer 1

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Subtracting 1010 from both sides gives x2−6x=−10,x2−6x=−10, which can be rewritten as x(x−6)=−10.x(x−6)=−10.Now use the variable change y=x−3y=x−3 (note that x−3x−3 is the midpoint of xx and x−6)x−6) to symmetrize the equation, getting (y+3)(y−3)=−10.(y+3)(y−3)=−10.Expanding, we get y2−9=−10,y2−9=−10, and adding 1010 to both sides gives y2=−1,y2=−1, which has no real solution. (Note that if there had been a real solution for x,x, say x=r,x=r, then y=r+3

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