-
The quadratic equation with rational coefficients, whose one root is √5, is :
-
- x 2 + 5 = 0
- x 2 - 10 = 0
- x 2 - 5 = 0
- None of these
- x 2 + 5 = 0
Correct Option: C
As per the given above question , we have
Let k1 and k2 be the roots of quadratic equation .
One root is k1 = √5
So the other root is k2 = − √5
∴ Sum of the roots = k1 + k2 = √5 + ( -√5 ) = 0
and product of the roots = k1 × k2 = − (√5) (- √5) = −5
∴ Required equation is x2 - (sum of the roots)x + (product of the roots) = 0
⇒ x2 - 5 = 0.
