Question

In the following, determine whether the given quadratic equation has real roots and if so, find the roots. [3 MARKS]

$6x^2+x-2=0$

Answer 1

Concept: 1 Mark
Formula: 1 Mark
Answer: 1 Mark

The given equation is $6x^2+x-2=0$

Here, $a=6,b=1andc=-2$

$\therefore D=b^2-4ac=1-4\times 6\times (-2)=49$

$\Rightarrow D>0$

So, the given equation has real roots. Roots are,

$\alpha =\frac{-b+\sqrt{D}}{2a}=\frac{-1+\sqrt{49}}{2\times 6}=\frac{-1+7}{12}=\frac{6}{12}=\frac{1}{2}$

and, $\beta =\frac{-b-\sqrt{D}}{2a}=\frac{-1-\sqrt{49}}{2\times 6}=\frac{-1-7}{12}=\frac{-8}{12}=\frac{-2}{3}$