Question

if one root of quadratic equation is 5+√5 then the product of roots is ??​

Answer 1

Step-by-step explanation:

If the given root is complex, then it’s conjugate will be the other root. So, if a+ib is a root, then a−ib is also a root.

If the given root is a surd of the form a+b√, then a−b√ is also a root.

If the root given is rational, then we can use the product of the roots rule.

The product of the roots of the quadratic equation ax2+bx+c=0 is ca.

So, in this case, we can find the other root by dividing this product by the given root.

If the co-efficient of x2 is ‘1’ (i.e.a=1), then this becomes much easier. You just need to divide the constant term of the quadratic by the known root.

Example: If one root of the quadratic equation x2−14x+45=0 is given as 5, then the other root is 455=9.

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