The quadratic equations $x^{2} - 5 x + 3 = 0$ has

no real roots

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two distinct real roots

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two equal real roots

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more than two real roots

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Solution

The correct option is B two distinct real roots
The nature of roots of the equation can be given by,
$D = b^{2} 4 a c = 0,$
For equation $x^{2} - 5 x + 3 = 0$ ,
$D = (- 5)^{2} - 4 (3) (1)$
$D = 13 > 0$ ,
It has two distinct real roots.

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Similar questions

Question 8
The quadratic equation $2 x^{2} - \sqrt{5} x + 1 = 0$ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots

Find the discriminant of the quadratic equation $3 x^{2} - 5 x + 2 = 0$ and find the nature of their roots.

α

and

β

are roots of the quadratic equation

a x^{2} + b x + c = 0

. The equation has real roots which are of opposite signs, then the equation

α (x - β)^{2} + β (x - α)^{2} = 0

Q. The quadratic equation

x^{2} - 18 x + 81 = 0

has 2 distinct real root.

Q. If a and b are distinct real numbers, show that the quadratic equation

2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0

has no real roots.

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The quadratic equations x2−5x+3=0 has

The correct option is B two distinct real rootsThe nature of roots of the equation can be given by,D=b24ac=0,For equation x2−5x+3=0,D=(−5)2−4(3)(1)D=13>0,It has two distinct real roots.

The quadratic equations $x^{2} - 5 x + 3 = 0$ has

The correct option is B two distinct real roots
The nature of roots of the equation can be given by,
$D = b^{2} 4 a c = 0,$
For equation $x^{2} - 5 x + 3 = 0$ ,
$D = (- 5)^{2} - 4 (3) (1)$
$D = 13 > 0$ ,
It has two distinct real roots.