Obtain the roots of the following quadratic e | vedclass

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Question

(A) The given quadratic equation is $6x^{2} + x - 2 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 6$,$b = 1$,and $c = -

Vedclass · Accepted Answer

$1/2, -2/3$

Vedclass · Answer

(A) The given quadratic equation is $6x^{2} + x - 2 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 6$,$b = 1$,and $c = -2$.The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.First,calculate the discriminant $D = b^{2} - 4ac = (1)^{2} - 4(6)(-2) = 1 + 48 = 49$.Now,substitute the values into the formula:$x = \frac{-1 \pm \sqrt{49}}{2(6)}$$x = \frac{-1 \pm 7}{12}$Case $1$: $x = \frac{-1 + 7}{12} = \frac{6}{12} = \frac{1}{2}$.Case $2$: $x = \frac{-1 - 7}{12} = \frac{-8}{12} = -\frac{2}{3}$.Thus,the roots are $1/2$ and $-2/3$.

Obtain the roots of the following quadratic equation by using the quadratic formula: $6x^{2} + x - 2 = 0$.

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