Question

3x2+2√5x-5=0 determine whether the given quadratic equation have real roots and if so, find the roots

Answer 1

the answer is in the pic...

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Answer 2

Answer:

yes, the given equation has two real roots. The real roots are $\frac{\sqrt{5}}{3}$ and $-\sqrt{5}$.

Step-by-step explanation:

The given quadratic equation is

$3x^2+2\sqrt{5}x-5=0$

The discriminant is

$D=b^2-4ac$

$D=(2\sqrt{5}}^2-4(3)(-5)=20+60=80>0$

Since the value of discriminant is positive, therefore the given equation has two real roots.

$x=\frac{-b\pm \sqrt{D}}{2a}$

$x=\frac{-2\sqrt{5}\pm \sqrt{80}}{2(3)}$

$x=\frac{-2\sqrt{5}\pm 4\sqrt{5}}{6}$

$x=\frac{-2\sqrt{5}+4\sqrt{5}}{6},\frac{-2\sqrt{5}-4\sqrt{5}}{6}$

$x=\frac{\sqrt{5}}{3},-\sqrt{5}$

Therefor the given equation has two real roots. The real roots are $\frac{\sqrt{5}}{3}$ and $-\sqrt{5}$.