Use the quadratic formula to find the exact solutions.
-$$5 \mathrm { t } ^ { 2 } - 7 \mathrm { t } = 1$$

A) $- \frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i }$
B) $\frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i }$
C) $\frac { - 7 \pm \sqrt { 69 } } { 10 }$
D) $\frac { 7 \pm \sqrt { 69 } } { 10 }$

Question

Use the quadratic formula to find the exact solutions.
-$$5 \mathrm { t } ^ { 2 } - 7 \mathrm { t } = 1$$

A) $- \frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i }$
B) $\frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i }$
C) $\frac { - 7 \pm \sqrt { 69 } } { 10 }$
D) $\frac { 7 \pm \sqrt { 69 } } { 10 }$

Quizplus · Accepted Answer

The quadratic formula is: $$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$For the equation $5t^2 - 7t = 1$, $a = 5$, $b = -7$, and $c = -1$.Substituting these values into the quadratic formula, we get:$$t = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(5)(-1)}}{2(5)}$$$$t = \frac{7 \pm \sqrt{49 + 20}}{10}$$$$t = \frac{7 \pm \sqrt{69}}{10}$$Therefore, the exact solutions are $t = \frac{7 + \sqrt{69}}{10}$ and $t = \frac{7 - \sqrt{69}}{10}$.

Use the Quadratic Formula to Find the Exact Solutions 5t2−7t=15 \mathrm { t } ^ { 2 } - 7 \mathrm { t } = 15t2−7t=1

Use the Quadratic Formula to Find the Exact Solutions $5 \mathrm { t } ^ { 2 } - 7 \mathrm { t } = 1$