abc ≠ 0 & a, b, c ϵ R. If x1 is a root of a2x2+bx+c=0,x2 is a root of a2x2−bx−c=0 and x1>x2>0, then the equation a2x2+2bx+2c=0 has a root x3 such that
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Q3
If the equation x+ay+(a2−bc)=0 x+by+(b2−ca)=0 x+cy+(c2−ab)=0 Consider: ⎡⎢⎣1aa2−bc1bb2−ca1cc2−ab⎤⎥⎦=0
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Q4
Solve using quadratic formula, abx2−(a2+b2)x+ab=0
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Q5
Assertion :If the equation x2+bx+ca=0 and x2+cx+ab=0 have a common root, then their other root will satisfy the equation x2+ax+bc=0 Reason: If the equation x2=bx+ca=0 and x2+cx+ab=0 have a common root, then a+b+c=0