The equation $x^{2} + x - 5 = 0$ has two distinct real roots.

True

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False

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Solution

The correct option is A
True

The given equation is $x^{2} + x - 5 = 0$
On comparing with $a x^{2} + b x + c = 0$ , we get
a = 1, b = 1 and c = -5
The discriminant of $x^{2} + x - 5 = 0$ is
$D = b^{2} - 4 a c = (1)^{2} - 4 (1) (- 5) = 1 + 20 = 21 \Rightarrow b^{2} - 4 a c > 0$
So, $x^{2} + x - 5 = 0$ has two distinct real roots.

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The equation x2+x−5=0 has two distinct real roots.

The correct option is A True The given equation is x2+x−5=0 On comparing with ax2+bx+c=0, we get a = 1, b = 1 and c = -5 The discriminant of x2+x−5=0 is D=b2−4ac=(1)2−4(1)(−5)=1+20=21⇒b2−4ac>0 So, x2+x−5=0 has two distinct real roots.

The equation $x^{2} + x - 5 = 0$ has two distinct real roots.