Question

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Answer 1

The other solution to the equation is -3.

Step-by-step explanation:

Given equation is;

5x²+bx+12=0

One solution is -4/5

We will put this solution in Eqn to get the value of b first,

$5(\frac{-4}{5})^2+b(\frac{-4}{5})+12=0\\5(\frac{16}{25})+(\frac{-4b}{5})+12=0\\\frac{16}{5}-\frac{-4b}{5}=-12$

Multiplying each term by 5

$5*(\frac{16}{5})-\frac{-4b}{5}*5=-12*5\\16-4b=-60\\-4b=-60-16\\-4b=-76$

Dividing both sides by -4

$\frac{-4b}{-4}=\frac{-76}{-4}\\b=19$

Putting b=19 in given Eqn

5x²+19x+12=0

Here,

a=5 , b=19 , c=12

Using quadratic formula,

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\x=\frac{-(19)\±\sqrt{(19)^2-4(5)(12)}}{2(5)}\\\\x=\frac{-19\±\sqrt{361-240}}{10}\\\\x=\frac{-19\±11}{10}$

Either,                   or,

$x=\frac{-19+11}{10},\ \ \ \ \ \ x=\frac{-19-11}{10}\\x=\frac{-8}{10},\ \ \ \ \ \ \ \ \ x=\frac{-30}{10}\\x=\frac{-4}{5},\ \ \ \ \ \ \ \ \ \ x= -3$

The other solution to the equation is -3.

Keywords: linear equation, quadratic formula

Learn more about quadratic formula at:

• brainly.com/question/7128279
• brainly.com/question/6788996

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