Question

Solve for x.....................

Answer 1

Answer:

C. $x=\frac{7}{3}$ and $x=\frac{-3}{2}$

Step-by-step explanation:

We have the quadratic equation $6x^{2}-5x-21=0$.

Now, the roots of the quadratic equation $ax^{2}+bx+c=0$ are given by $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$.

So, from the given equation, we have,

a = 6, b = -5, c = -21.

Substituting the values in $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$, we get,

$x=\frac{5\pm \sqrt{(-5)^{2}-4\times 6\times (-21)}}{2\times 6}$

i.e. $x=\frac{5\pm \sqrt{25+504}}{12}$

i.e. $x=\frac{5\pm \sqrt{529}}{12}$

i.e. $x=\frac{5\pm 23}{12}$

i.e. $x=\frac{5+23}{12}$ and i.e. $x=\frac{5-23}{12}$

i.e. $x=\frac{28}{12}$ and i.e. $x=\frac{-18}{12}$

i.e. $x=\frac{7}{3}$ and i.e. $x=\frac{-3}{2}$

Thus, the value for x are $\frac{7}{3}$ and $\frac{-3}{2}$

Answer 2

Answer:

Option C is correct, i.e. x = 7/3, x = -3/2.

Step-by-step explanation:

Given the equation is 6x² -5x + -21 = 0.

Then a = 6, b = -5, c = -21

Using the Quadratic formula, x = ( -b ± √(b² -4ac) )/2a

x = ( +5 ± √((-5)² -4*6*-21) )/2*6

x = ( 5 ± √(25 +504) )/12

x = ( 5 ± √(529) )/12

x = ( 5 ± 23 )/12

x = (5-23)/12 or x = (5+23)/12

x = -18/12 or x = 28/12

x = -3/2 or x = 7/3

Hence, option C is correct, i.e. x = 7/3, x = -3/2.