Solve the following equation using the quadra | vedclass

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Question

(A) For the quadratic equation $ax^{2} + bx + c = 0$,the quadratic formula is $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Here,$a = 5$,$b = -3$,and $c

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$-\frac{2}{5}, 1$

Vedclass · Answer

(A) For the quadratic equation $ax^{2} + bx + c = 0$,the quadratic formula is $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Here,$a = 5$,$b = -3$,and $c = -2$.First,calculate the discriminant $D = b^{2} - 4ac = (-3)^{2} - 4(5)(-2) = 9 + 40 = 49$.Since $D > 0$,real solutions exist.Applying the formula: $x = \frac{-(-3) \pm \sqrt{49}}{2(5)} = \frac{3 \pm 7}{10}$.Case $1$: $x = \frac{3 + 7}{10} = \frac{10}{10} = 1$.Case $2$: $x = \frac{3 - 7}{10} = \frac{-4}{10} = -\frac{2}{5}$.Thus,the solutions are $-\frac{2}{5}$ and $1$.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $5x^{2} - 3x - 2 = 0$.

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