Question

If one of the roots of a quadratic
equation having rational
coefficients is ✓7-4, then the
quadratic equation is​

Answer 1

Answer:

if x=a+b√ is a root of an arbitrary polynomial equation p(x)=0, then x=a−b√ is also a root of p(x)=0

If α and β are roots of a quadratic equation, then using Vieta’s rules the quadratic equation is given by x2−(α+β)x+αβ=0

α=−4+7–√⟹β=−4−7–√(Irrational Conjugate Theorem)

x2−(α+β)x+αβx2−(−4+7–√−4−7–√)x+(−4+7–√)(−4−7–√)x2+8x−(7–√+4)(7–√−4)x2+8x−(7−16)x2+8x+9=0=0=0=0=0

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