Question

One solution of 10x^2 + bx – 3 = 0 is - 4/5 Find b and the other solution.
What is the value of b in the equation?​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given that x = - $\frac{4}{5}$ is a solution of the equation

Then substitute this value into the equation and solve for b

10 ( - $\frac{4}{5}$ )² + b(- $\frac{4}{5}$ ) - 3 = 0

10 × $\frac{16}{25}$ - $\frac{4}{5}$ b - 3 = 0

$\frac{32}{5}$ - $\frac{4}{5}$ b - 3 = 0

Multiply through by 5

32 - 4b - 15 = 0

17 - 4b = 0 ( subtract 17 from both sides )

- 4b = - 17 ( divide both sides by - 4 )

b = $\frac{17}{4}$ ← value of b

Given α and β are the roots of a quadratic equation, then

α + β = - $\frac{b}{a}$

let α = - $\frac{4}{5}$, then with a = 10 and b = b

- $\frac{4}{5}$ + β = - $\frac{\frac{17}{4} }{10}$ = - $\frac{17}{40}$

β = - $\frac{17}{40}$ + $\frac{4}{5}$ = $\frac{3}{8}$

Hence the other solution is x = $\frac{3}{8}$