Question

find the nature of roots of the quadratic equation x²-2√5x+5=0 class10​

Answer 1

Answer :

Real and equal roots

Step-by-step explanation :

$Given \ quadratic \ equation, \\x^{2} -2\sqrt{5}x+5=0 \\\\ it \ is \ of \ the \ form \ ax^2+bx+c=0 \\a=1,b=-2\sqrt{5},c=5 \\\\ \boxed{Discriminant,D=b^2-4ac } \\\\ D=(-2\sqrt{5})^2-4(1)(5) \\ D=4(5)-20\\D=20-20\\D=0 \\\\ \implies \text{It has real and equal roots}$

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NATURE OF ROOTS :

If D < 0 ; no real roots

If D = 0 ; real and equal roots

If D > 0 ; real and unequal roots