Question

The roots of the equation 3x^2-12x+10=0 are irrational and unequal.

Answer 1

Answer

True

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Answer 2

Given quadratic equation $3x^2-12x+10=0$

The roots of the quadratic equation $ax^2+bx+c=0$ is,

$x=\frac{-b\pm\sqrt{\left( {{b}^{2}}-4ac \right)}}{2a}$

Where a=3, b= -12 and c=10

$x=\frac{-(-12)\pm\sqrt{\left( {{-12}^{2}}-4(3)(10) \right)}}{2(3)}\\x=\frac{12\pm\sqrt{\left( 144-120 \right)}}{6}\\x=\frac{12\pm\sqrt{24}}{6}\\x=\frac{12\pm2\sqrt{6}}{6}\\x=\frac{6\pm\sqrt{6}}{3}$

The irrational and unequal roots are $x=\frac{6+\sqrt{6}}{3}, x=\frac{6-\sqrt{6}}{3}$